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1
GUARNOTTA, Umberto. "EXISTENCE RESULTS FOR SINGULAR CONVECTIVE ELLIPTIC PROBLEMS." Doctoral thesis, Università degli Studi di Palermo, 2021. http://hdl.handle.net/10447/524941.
Повний текст джерела
2
Murillo, Kelly Patricia. "Existence results for elliptic equations with singular terms." Doctoral thesis, Universidade de Aveiro, 2013. http://hdl.handle.net/10773/9888.
Повний текст джерелаАнотація:
Doutoramento em Matemática e AplicaçõesEsta dissertação estuda em detalhe três problemas elípticos: (I) uma classe de equações que envolve o operador Laplaciano, um termo singular e nãolinearidade com o exponente crítico de Sobolev, (II) uma classe de equações com singularidade dupla, o expoente crítico de Hardy-Sobolev e um termo côncavo e (III) uma classe de equações em forma divergente, que envolve um termo singular, um operador do tipo Leray-Lions, e uma função definida nos espaços de Lorentz. As não-linearidades consideradas nos problemas (I) e (II), apresentam dificuldades adicionais, tais como uma singularidade forte no ponto zero (de modo que um "blow-up" pode ocorrer) e a falta de compacidade, devido à presença do exponente crítico de Sobolev (problema (I)) e Hardy-Sobolev (problema (II)). Pela singularidade existente no problema (III), a definição padrão de solução fraca pode não fazer sentido, por isso, é introduzida uma noção especial de solução fraca em subconjuntos abertos do domínio. Métodos variacionais e técnicas da Teoria de Pontos Críticos são usados para provar a existência de soluções nos dois primeiros problemas. No problema (I), são usadas uma combinação adequada de técnicas de Nehari, o princípio variacional de Ekeland, métodos de minimax, um argumento de translação e estimativas integrais do nível de energia. Neste caso, demonstramos a existência de (pelo menos) quatro soluções não triviais onde pelo menos uma delas muda de sinal. No problema (II), usando o método de concentração de compacidade e o teorema de passagem de montanha, demostramos a existência de pelo menos duas soluções positivas e pelo menos um par de soluções com mudança de sinal. A abordagem do problema (III) combina um resultado de surjectividade para operadores monótonos, coercivos e radialmente contínuos com propriedades especiais do operador de tipo Leray- Lions. Demonstramos assim a existência de pelo menos, uma solução no espaço de Lorentz e obtemos uma estimativa para esta solução.
This dissertation study mainly three elliptical problems: (I) a class of equations, which involves the Laplacian operator, a singular term and a nonlinearity with the critical Sobolev exponent, (II) a class of equations with double singularity, the critical Hardy-Sobolev exponent and a concave term and (III) a class of equations in divergent form, which involves a singular term, a Leray-Lions operator, and a function defined on Lorentz spaces. The nonlinearities considered in problems (I) and (II), bring additional difficulties which, as the strong singularity at zero (so blow-up may occur) and the lack of compactness due to the presence of a Sobolev critical exponent (problem (I)) and a Hardy-Sobolev critical exponent (problem (II)). In problem (III), the singularity implies that the standard definition of weak solution may not make sense. Therefore is necessary to introduce a special notion of weak solution on open subsets of the domain. Variational methods and Critical Point Theory techniques are used to prove the existence of solutions in the two first problems. In problem (I), our method combines Nehari's techniques, Ekeland's variational principle, minimax methods, a translation argument and integral estimates of the energy level. In this case, we prove the existence of (at least) four nontrivial solutions where at least one of them is sign-changing. In problem (II), we prove the existence of at least two positive solutions and a pair of sign-changing solutions, using the concentration-compactness method and the mountain pass theorem. The approach in problem (III) combines a surjectivity result for monotone, coercive and radially continuous operators with special properties of Leray-Lions operators. We prove the existence of at least one solution in a Lorentz space and obtain an estimative for the solution.
3
Fialho, João Manuel Ferrão. "Existence, localization and multiplicity results for nonlinear and functional." Doctoral thesis, Universidade de Évora, 2012. http://hdl.handle.net/10174/15248.
Повний текст джерелаАнотація:
In this thesis several problems are addressed. The problems considered vary
from second order problems up to high order problems where generaliza-
tions to nth order are studied. Such problems range from problems without
functional dependence up to problems where the functional dependence is
featured both in the equation and on the boundary conditions.
Functional boundary conditions include most of the classical conditions
as multipoint cases, conditions with delay and/or advances, nonlocal or in-
tegral, with maximum or minimum arguments,... Existence, nonexistence,
multiplicity and localization results are then discussed in accordance with
these conditions.
The method used is the lower and upper solutions combined with di¤erent
techniques (degree theory, Nagumo condition, iterative technique, Green s
function) to obtain such results.
Several applications are studied such as the periodic oscillations of the
axis of a satellite and conjugate boundary value problems, to emphasize the
applicability of the method used; RESUMO:Nesta tese, intitulada em português, Resultados de existência, localiza-
ção e multiplicidade para problemas não lineares e funcionais de ordem su-
perior com valores na fronteira , diferentes problemas são abordados. Estes
problemas variam desde problemas de segunda ordem até problemas de or-
dem superior, onde generalizações de ordem n são feitas e onde os problemas
apresentados variam desde o caso em que não existe dependência funcional
até aos em que esta dependência funcional está presente tanto na equação
como nas condições de fronteira.
Sobre estas condições, que incluem a maioria das condições clássicas, re-
sultados de existência, não existência, multiplicidade e localização de solução
são discutidos de acordo com estas condições.
O método utilizado é o método da sub e sobre-solução combinado com
diferentes técnicas.
Várias aplicações são estudadas, nomeadamente as oscilações periódicas
do eixo de um satélite e problemas conjugados, de forma a dar ênfase à
aplicabilidade do método utilizado.
4
Velichkov, Bozhidar. "Existence and regularity results for some shape optimization problems." Doctoral thesis, Scuola Normale Superiore, 2013. http://hdl.handle.net/11384/85690.
Повний текст джерелаАнотація:
Les problèmes d'optimisation de forme sont présents naturellement en physique, ingénierie, biologie, etc. Ils visent à répondre à différentes questions telles que:-A quoi une aile d'avion parfaite pourrait ressembler?-Comment faire pour réduire la résistance d'un objet en mouvement dans un gaz ou un fluide?-Comment construire une structure élastique de rigidité maximale?-Quel est le comportement d'un système de cellules en interaction?Pour des exemples précis et autres applications de l'optimisation de forme nous renvoyons à [20] et [69]. Ici, nous traitons les aspects mathématiques théoriques de l'optimisation de forme, concernant l'existence d'ensembles optimaux ainsi que leur régularité. Dans toutes les situations que l'on considère, la fonctionnelle dépend de la solution d'une certaine équation aux dérivées partielles posée sur la forme inconnue. Nous allons parfois se référer à cette fonction comme une fonction d'état.Les fonctions d'état les plus simples, mais qui apparaissent dans beaucoup de problèmes, sont données par les solutions des équations -Δw = 1 et -Δu = λu,qui sont liées à la torsion et aux modes d'oscillation d'un objet donné. Notre étude se concentrera principalement sur ces fonctionnelles de formes, impliquant la torsion et le spectre.[20] D. Bucur, G. Buttazzo: Variational Methods in Shape Optimization Problems. Progress in Nonlinear Differential Equations 65, Birkhauser Verlag, Basel (2005).[69] A. Henrot, M. Pierre: Variation et optimisation de formes: une analyse geometrique. Springer-Berlag, Berlin, 2005The shape optimization problems naturally appear in engineering and biology. They aim to answer questions as:-What a perfect wing may look like?-How to minimize the resistance of a moving object in a gas or a fluid?-How to build a rod of maximal rigidity?-What is the behaviour of a system of cells?The shape optimization appears also in physics, mainly in electrodynamics and in the systems presenting both classical and quantum mechanics behaviour. For explicit examples and furtheraccount on the applications of the shape optimization we refer to the books [20] and [69]. Here we deal with the theoretical mathematical aspects of the shape optimization, concerning existence of optimal sets and their regularity. In all the practical situations above, the shape of the object in study is determined by a functional depending on the solution of a given partial differential equation. We will sometimes refer to this function as a state function.The simplest state functions are provided by solutions of the equations−∆w = 1 and −∆u = λu,which usually represent the torsion rigidity and the oscillation modes of a given object. Thus our study will be concentrated mainly on the situations, in which these state functions appear,i.e. when the optimality is intended with respect to energy and spectral functionals. [20] D. Bucur, G. Buttazzo: Variational Methods in Shape Optimization Problems. Progress in Nonlinear Differential Equations 65, Birkhauser Verlag, Basel (2005).[69] A. Henrot, M. Pierre: Variation et optimisation de formes: une analyse geometrique. Springer-Berlag, Berlin, 2005
5
Velichkov, Bozhidar. "Existence and regularity results for some shape optimization problems." Thesis, Grenoble, 2013. http://www.theses.fr/2013GRENM088/document.
Повний текст джерелаАнотація:
Les problèmes d'optimisation de forme sont présents naturellement en physique, ingénierie, biologie, etc. Ils visent à répondre à différentes questions telles que:-A quoi une aile d'avion parfaite pourrait ressembler?-Comment faire pour réduire la résistance d'un objet en mouvement dans un gaz ou un fluide?-Comment construire une structure élastique de rigidité maximale?-Quel est le comportement d'un système de cellules en interaction?Pour des exemples précis et autres applications de l'optimisation de forme nous renvoyons à [20] et [69]. Ici, nous traitons les aspects mathématiques théoriques de l'optimisation de forme, concernant l'existence d'ensembles optimaux ainsi que leur régularité. Dans toutes les situations que l'on considère, la fonctionnelle dépend de la solution d'une certaine équation aux dérivées partielles posée sur la forme inconnue. Nous allons parfois se référer à cette fonction comme une fonction d'état.Les fonctions d'état les plus simples, mais qui apparaissent dans beaucoup de problèmes, sont données par les solutions des équations -Δw = 1 et -Δu = λu,qui sont liées à la torsion et aux modes d'oscillation d'un objet donné. Notre étude se concentrera principalement sur ces fonctionnelles de formes, impliquant la torsion et le spectre.[20] D. Bucur, G. Buttazzo: Variational Methods in Shape Optimization Problems. Progress in Nonlinear Differential Equations 65, Birkhauser Verlag, Basel (2005).[69] A. Henrot, M. Pierre: Variation et optimisation de formes: une analyse geometrique. Springer-Berlag, Berlin, 2005The shape optimization problems naturally appear in engineering and biology. They aim to answer questions as:-What a perfect wing may look like?-How to minimize the resistance of a moving object in a gas or a fluid?-How to build a rod of maximal rigidity?-What is the behaviour of a system of cells?The shape optimization appears also in physics, mainly in electrodynamics and in the systems presenting both classical and quantum mechanics behaviour. For explicit examples and furtheraccount on the applications of the shape optimization we refer to the books [20] and [69]. Here we deal with the theoretical mathematical aspects of the shape optimization, concerning existence of optimal sets and their regularity. In all the practical situations above, the shape of the object in study is determined by a functional depending on the solution of a given partial differential equation. We will sometimes refer to this function as a state function.The simplest state functions are provided by solutions of the equations−∆w = 1 and −∆u = λu,which usually represent the torsion rigidity and the oscillation modes of a given object. Thus our study will be concentrated mainly on the situations, in which these state functions appear,i.e. when the optimality is intended with respect to energy and spectral functionals. [20] D. Bucur, G. Buttazzo: Variational Methods in Shape Optimization Problems. Progress in Nonlinear Differential Equations 65, Birkhauser Verlag, Basel (2005).[69] A. Henrot, M. Pierre: Variation et optimisation de formes: une analyse geometrique. Springer-Berlag, Berlin, 2005
6
Platino, Vincenzo. "Existence, regularity and testability results in economic models with externalities." Doctoral thesis, Universita degli studi di Salerno, 2012. http://hdl.handle.net/10556/1312.
Повний текст джерелаАнотація:
2008 - 2009This thesis deals with economic models in the presence of externalities. The thesis consists of three chapters. In chapter 1, we consider a general model of production economies with consumption and production externalities. That is, the choices of all agents (households and firms) affect individual consumption sets, individual preferences and production technologies. Describing equlibria in terms of first order conditions and market clearing conditions, and using a homotopy, under differentiability and boundary conditions, we prove the non-emptiness and compactness of the set of competitive equilibria with consumptions and prices strictly positive. In chapter 2 we consider a general model of private ownership economies with consumption and production externalities. Showing by an example that basic assumptions are not enough to guarantee a regularity result in the space of initial endowments, we provide sufficient conditions for the regularity in the space of endowments and transformation functions. In chapter 3 we study the testability implications of public versus private consumption in collective models of group consumption. To the contrary at the previous literature, we find that assumptions regarding the public or private nature of specific goods do have testability implications, even if one only observes the aggregate group consumption. In fact, these testability implications apply as soon as the analysis includes three goods and four observations. In our opinion, our revealed preference approach obtains stronger testability conclusions because it focuses on conditions which involve personalized prices and personalized quantities, although we do not require that personalized prices and personalized quantities are observable. [edited by author]
VIII n.s.
7
Malchiodi, Andrea. "Existence and multiplicity results for some problems in Riemannian geometry." Doctoral thesis, SISSA, 2000. http://hdl.handle.net/20.500.11767/4627.
Повний текст джерела
8
Manicom, Gray Thomas. "Existence results for a class of semi-linear initial value problems." Diss., University of Pretoria, 2017. http://hdl.handle.net/2263/63288.
Повний текст джерелаАнотація:
The main result of this thesis is an existence result for parabolic semi-linear
problems. This is done by reformulating the semi-linear problem as an abstract
Cauchy problem
ut(t) = Au(t) + f(t; u(t)), t > 0
u(0) = u0 (1)
for u0 2 X, where X is a Banach space. We then develop and use the theory
of compact semigroups to prove an existence result.
In order to make this result applicable, we give a characterization of
compact semigroups in terms of its resolvent operator and continuity in the
uniform operator topology. Thus, using the theory of analytic semigroups,
we are able to determine under what conditions on A a solution to (1) exists.
Furthermore, we consider the asymptotic behaviour and regularity of such
solutions. By developing perturbation theory, we are easily able to apply our
existence result to a larger class of problems. We then demonstrate these
results with an example.
This work is signi cant in providing a novel approach to a group of previously
established results. The content can be considered pure mathematics,
but it is of signi cant importance in real world situations. The structure
of the thesis, and the choice of certain de nitions, lends itself to be easily
understood and interpreted in the light of these real world situations and
is intended to be easily followed by an applied mathematician. An important
part of this process is to develop the problem in a real Hilbert space
and then to consider the complexi cation of the problem in order to reset
it in a complex Hilbert space, in which we can apply the theory of analytic
semigroups. A large number of real world problems fall into the class of
problems discussed here, not only in biology as demonstrated, but also in
physics, chemistry, and elsewhere.Dissertation (MSc)--University of Pretoria, 2017.
Mathematics and Applied Mathematics
MSc
Unrestricted
9
Sfecci, Andrea. "Some existence results for boundary value problems : a promenade along resonance." Doctoral thesis, SISSA, 2012. http://hdl.handle.net/20.500.11767/4703.
Повний текст джерелаАнотація:
I present many existence result to many boundary value problems, in particular periodic problems and Neumann elliptic problems. The results use the method of the topological degree theory. In the thesis different problems are treated: planar systems, systems with a singularity, impact oscillators, coupled oscillators and radial elliptic problems.
10
Sauer, Martin [Verfasser]. "Existence and Uniqueness Results for Randomly Forced Generalized Newtonian Fluids / Martin Sauer." München : Verlag Dr. Hut, 2013. http://d-nb.info/1034003283/34.
Повний текст джерела
11
Nerlich, Alexander [Verfasser]. "Adding randomness to nonlinear semigroups: existence, uniqueness and asymptotic results / Alexander Nerlich." Ulm : Universität Ulm, 2018. http://d-nb.info/1171900880/34.
Повний текст джерела
12
Luo, Yongming [Verfasser]. "Existence and Regularity Results of a Ferroelectric Phase-Field Model / Yongming Luo." Kassel : Universitätsbibliothek Kassel, 2019. http://d-nb.info/1201508339/34.
Повний текст джерела
13
Meinert, Melissa [Verfasser]. "Partial differential equations on fractals. Existence, Uniqueness and Approximation results / Melissa Meinert." Bielefeld : Universitätsbibliothek Bielefeld, 2020. http://d-nb.info/1214806538/34.
Повний текст джерела
14
Hebestreit, Niklas [Verfasser], Christiane [Gutachter] Tammer, and Franco [Gutachter] Giannessi. "Existence results for vector quasi-variational problems / Niklas Hebestreit ; Gutachter: Christiane Tammer, Franco Giannessi." Halle (Saale) : Universitäts- und Landesbibliothek Sachsen-Anhalt, 2020. http://d-nb.info/122159981X/34.
Повний текст джерела
15
Araújo, Yane Lísley Ramos. "Existence results for some elliptic equations involving the fractional Laplacian operator and critical growth." Universidade Federal da Paraíba, 2015. http://tede.biblioteca.ufpb.br:8080/handle/tede/9252.
Повний текст джерелаАнотація:
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In this work we prove some results of existence and multiplicity of solutions for equations of the type ( ) u + V (x)u = f(x; u) in RN; where 0 < < 1, N 2 , ( ) denotes the fractional Laplacian, V : RN ! R is a continuous function that satisfy suitable conditions and f : RN R ! R is a continuous function that may have critical growth in the sense of the Trudinger-Moser inequality or in the sense of the critical Sobolev exponent. In order to obtain our results we use variational methods combined with a version of the Concentration-Compactness Principle due to Lions.
Neste trabalho provamos alguns resultados de existência e multiplicidade de soluções para equações do tipo ( ) u + V (x)u = f(x; u) em RN; onde 0 < < 1, N 2 , ( ) denota o Laplaciano fracionário, V : RN ! R é uma função contínua que satisfaz adequadas condições e f : RN R ! R é uma função cont ínua que pode ter crescimento crítico no sentido da desigualdade de Trudinger-Moser ou no sentido do expoente crítico de Sobolev. A m de obter nossos resultados usamos métodos variacionais combinados com uma versão do Princípio de Concentração- Compacidade devido à Lions.
16
Cabarrubias, Bituin C. "Existence, uniqueness and homogenization results for a class of nonlinear PDE in perforated domains." Rouen, 2012. http://www.theses.fr/2012ROUES046.
Повний текст джерелаАнотація:
This thesis is devoted to the existence, uniqueness and homogenization results for a quasilinear elliptic problem with oscillating coefficients and with nonlinear Robin boundary condition in a periodically perforated domain. A suitable frowth conditions are assumed on the nonlinear boundary term and on the quasilinear term, some assumptions on the modulus of continuity introduced in Chipot [17] and weaker than a Lipschitz condition, are prescribed. For the existence and uniqueness of a solution, we consider a more general framework which, in particular, will imply the existence and uniqueness of the solution of the problem. To deal with the existence of a solution, we prove first the weak continuity of the boundary nonlinear operator which is a difficult part. Together with this property, we use the Schauder's Fixed Point Theorem to show the existence. For the uniqueness, we adapt to our situation some arguments introduced in André-Chipot [5] (see also chapter 11 of [17] for Dirichlet conditions) and partially extended to linear Robin conditions in Bendib-Tcheugoué Tébou [11] and Bendib [10]. For the homogenization of the problem, we study the convergence to a limit problem using the Periodic Unfolding Method in perforated domains. Here, we proved related properties of the onfolding operators which are needed in the process. We also show the well-posedness of the limit system by proving that the homogenized operator inherits the modulus of continuity of the initial problem. As a consequence, the uniqueness of a solution of the homogenized quasilinear problem follows. A corrector result is also obtained using this method.
17
Tian, Rushun. "Existence and Multiplicity Results on Standing Wave Solutions of Some Coupled Nonlinear Schrodinger Equations." DigitalCommons@USU, 2013. https://digitalcommons.usu.edu/etd/1484.
Повний текст джерелаАнотація:
Coupled nonlinear Schrodinger equations (CNLS) govern many physical phenomena, such as nonlinear optics and Bose-Einstein condensates. For their wide applications, many studies have been carried out by physicists, mathematicians and engineers from different respects. In this dissertation, we focused on standing wave solutions, which are of particular interests for their relatively simple form and the important roles they play in studying other wave solutions. We studied the multiplicity of this type of solutions of CNLS via variational methods and bifurcation methods.
Variational methods are useful tools for studying differential equations and systems of differential equations that possess the so-called variational structure. For such an equation or system, a weak solution can be found through finding the critical point of a corresponding energy functional. If this equation or system is also invariant under a certain symmetric group, multiple solutions are often expected. In this work, an integer-valued function that measures symmetries of CNLS was used to determine critical values. Besides variational methods, bifurcation methods may also be used to find solutions of a differential equation or system, if some trivial solution branch exists and the system is degenerate somewhere on this branch. If local bifurcations exist, then new solutions can be found in a neighborhood of each bifurcation point. If global bifurcation branches exist, then there is a continuous solution branch emanating from each bifurcation point.
We consider two types of CNLS. First, for a fully symmetric system, we introduce a new index and use it to construct a sequence of critical energy levels. Using variational methods and the symmetric structure, we prove that there is at least one solution on each one of these critical energy levels. Second, we study the bifurcation phenomena of a two-equation asymmetric system. All these bifurcations take place with respect to a positive solution branch that is already known. The locations of the bifurcation points are determined through an equation of a coupling parameter. A few nonexistence results of positive solutions are also given
18
Yusuf, Owolabi. "On models of Kirchhoff Equations with damping terms: existence results and asymptotic behaviour of solutions." Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29370.
Повний текст джерела
19
MONTANARI, Piera. "Local and Global Existence results for the Characteristic Problem for Linear and Semi-linear Wave Equations." Doctoral thesis, Università degli studi di Ferrara, 2010. http://hdl.handle.net/11392/2389334.
Повний текст джерелаАнотація:
The thesis concerns the well posedness of the Characteristic Initial
Value Problem for the Semilinear Wave Equation, with initial data on
a light cone. In the first part of the thesis, an explicit representation
formula for the solution of the linear equation is given, extending the
results known for the homogeneous equation and the trace on the time
axis of the solution.
Further, Energy Estimates are derived. In constructing such Estimates
one encounters several difficulties due to the presence of a
geometrical singularity at the tip of the cone. To manage the construction
of the Energy Estimate, one introduces suitable Sobolev-like
norms characterized by weights, which mitigates the difficulties in the
origin. These Estimates are well posed only for functions which vanish
of order high enough at the origin. This fact brings us to split the initial
data in the sum of two terms. The first term consists of the Taylor
polynomial of the initial datum, the second one consist of remainder
regular function with the required vanishing order at the origin.
An interesting phenomenon observed here is a gap of differentiability
between the solution and the initial data.
The solution obtained using the Energy method is still incomplete,
because of the splitting of the initial data. This fact brings us to solve
the problem for purely polynomial data. For this purpose, it is used a
generalization of the well-known harmonic polynomials.
The last part of the thesis is devoted to the semi-linear problem,
for which the tools developed in the previous chapters are generalized.
20
Azizieh, Céline. "A priori estimates, continuation methods and existence results for positive solutions of p-Laplace eauqations and systems." Doctoral thesis, Universite Libre de Bruxelles, 2001. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211660.
Повний текст джерела
21
Mazzoleni, Dario [Verfasser], Aldo [Akademischer Betreuer] Pratelli, Dorin [Akademischer Betreuer] Bucur, and Giuseppe [Akademischer Betreuer] Buttazzo. "Existence and regularity results for solutions of spectral problems / Dario Mazzoleni. Gutachter: Aldo Pratelli ; Dorin Bucur ; Giuseppe Buttazzo." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2014. http://d-nb.info/1065270380/34.
Повний текст джерела
22
Feltrin, Guglielmo. "Positive solutions to indefinite problems: a topological approach." Doctoral thesis, SISSA, 2016. http://hdl.handle.net/2318/1655560.
Повний текст джерелаАнотація:
The present Ph.D. thesis is devoted to the study of positive solutions to indefinite problems. In particular, we deal with the second order nonlinear differential equation u'' + a(t) g(u) = 0, where g : [0,+∞[→[0,+∞[ is a continuous nonlinearity and a : [0,T]→R is a Lebesgue integrable sign-changing weight. We analyze the Dirichlet, Neumann and periodic boundary value problems on [0,T] associated with the equation and we provide existence, nonexistence and multiplicity results for positive solutions. In the first part of the manuscript, we investigate nonlinearities g(u) with a superlinear growth at zero and at infinity (including the classical superlinear case g(u)=u^p, with p>1). In particular, we prove that there exist 2^m-1 positive solutions when a(t) has m positive humps separated by negative ones and the negative part of a(t) is sufficiently large. Then, for the Dirichlet problem, we solve a conjecture by Gómez‐Reñasco and López‐Gómez (JDE, 2000) and, for the periodic problem, we give a complete answer to a question raised by Butler (JDE, 1976). In the second part, we study the super-sublinear case (i.e. g(u) is superlinear at zero and sublinear at infinity). If a(t) has m positive humps separated by negative ones, we obtain the existence of 3^m-1 positive solutions of the boundary value problems associated with the parameter-dependent equation u'' + λ a(t) g(u) = 0, when both λ>0 and the negative part of a(t) are sufficiently large. We propose a new approach based on topological degree theory for locally compact operators on open possibly unbounded sets, which applies for Dirichlet, Neumann and periodic boundary conditions.
As a byproduct of our method, we obtain infinitely many subharmonic solutions and globally defined positive solutions with complex behavior, and we deal with chaotic dynamics. Moreover, we study positive radially symmetric solutions to the Dirichlet and Neumann problems associated with elliptic PDEs on annular domains. Furthermore, this innovative technique has the potential and the generality needed to deal with indefinite problems with more general differential operators. Indeed, our approach apply also for the non-Hamiltonian equation u'' + cu' + a(t) g(u) = 0. Meanwhile, more general operators in the one-dimensional case and problems involving PDEs will be subjects of future investigations.
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Hauser, Carlos [Verfasser], and W. [Akademischer Betreuer] Reichel. "Existence Results and A Priori Bounds for Positive Solutions of Discrete Nonlinear Elliptic Equations / Carlos Hauser ; Betreuer: W. Reichel." Karlsruhe : KIT-Bibliothek, 2019. http://d-nb.info/1190178923/34.
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Herán, Andreas [Verfasser], Jens [Akademischer Betreuer] Habermann, and Jens [Gutachter] Habermann. "Existence and Regularity Results for Parabolic Problems on Metric Measure Spaces / Andreas Herán ; Gutachter: Jens Habermann ; Betreuer: Jens Habermann." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2020. http://d-nb.info/1218785721/34.
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Schätzler, Leah [Verfasser], Frank [Akademischer Betreuer] Duzaar, and Frank [Gutachter] Duzaar. "Existence and Stability Results for Nonlinear and Doubly Nonlinear Evolutionary Problems / Leah Schätzler ; Gutachter: Frank Duzaar ; Betreuer: Frank Duzaar." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2020. http://d-nb.info/1216704287/34.
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Huang, Lirong. "Multiplicity results for some classes of Schrödinger-Poisson systems." Doctoral thesis, Universidade de Aveiro, 2014. http://hdl.handle.net/10773/12867.
Повний текст джерелаАнотація:
Doutoramento conjunto em Matemática - Matemática e Aplicações (PDMA)In this thesis, we study the existence and multiplicity of solutions of the following class of Schr odinger-Poisson systems: u + u + l(x) u = (x; u) in R3; = l(x)u2 in R3; where l 2 L2(R3) or l 2 L1(R3). And we consider that the nonlinearity satis es the following three kinds of cases: (i) a subcritical exponent with (x; u) = k(x)jujp2u + h(x)u (4 p < 2 ) under an inde nite case; (ii) a general inde nite nonlinearity with (x; u) = k(x)g(u) + h(x)u; (iii) a critical growth exponent with (x; u) = k(x)juj2 2u + h(x)jujq2u (2 q < 2 ). It is worth mentioning that the thesis contains three main innovations except overcoming several di culties, which are generated by the systems themselves. First, as an unknown referee said in his report, we are the rst authors concerning the existence of multiple positive solutions for Schr odinger- Poisson systems with an inde nite nonlinearity. Second, we nd an interesting phenomenon in Chapter 2 and Chapter 3 that we do not need the condition R R3 k(x)ep 1dx < 0 with an inde nite noncoercive case, where e1 is the rst eigenfunction of +id in H1(R3) with weight function h. A similar condition has been shown to be a su cient and necessary condition to the existence of positive solutions for semilinear elliptic equations with inde nite nonlinearity for a bounded domain (see e.g. Alama-Tarantello, Calc. Var. PDE 1 (1993), 439{475), or to be a su cient condition to the existence of positive solutions for semilinear elliptic equations with inde nite nonlinearity in RN (see e.g. Costa-Tehrani, Calc. Var. PDE 13 (2001), 159{189). Moreover, the process used in this case can be applied to study other aspects of the Schr odinger-Poisson systems and it gives a way to study the Kirchho system and quasilinear Schr odinger system. Finally, to get sign changing solutions in Chapter 5, we follow the spirit of Hirano-Shioji, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), 333, but the procedure is simpler than that they have proposed in their paper.
Nesta tese, estudamos a existência e a multiplicidade de soluções da seguinte classe de sistemas denominada de Schr odinger-Poisson: u + u + l(x) u = (x; u) in R3; = l(x)u2 in R3; onde l 2 L2(R3) ou l 2 L1(R3). Consideram-se não-linearidades que satisfazem um dos seguintes casos: (i) potências que envolvem um expoente sub-cr tico, da forma (x; u) = k(x)jujp2u + h(x)u, (4 p < 2 ), sendo k uma função com sinal indefinido e h uma função positiva; (ii) caso geral de uma não-linearidade indefi nida, da forma (x; u) = k(x)g(u) + h(x)u, sendo k uma função com sinal indefinido e h uma função positiva; (iii) potências que envolvem o expoente crí tico, da forma (x; u) = k(x)juj2 2u + h(x)jujq2u (2 q < 2 ). Convém salientar que esta tese tem três principais inovações, as quais ultrapassam dificuldades geradas pela natureza dos problemas estudados. Primeiro, como um relator anónimo referiu, este é o primeiro trabalho em que se trata a existência de várias soluções de sistemas de Schrödinger- Poisson com não-linearidade indefinida. Segundo, neste estudo encontrou-se um fen ómeno interessante, ver Capítulos 2 e 3, nomeadamente, não ser necess ária a condição R3 k(x)ep 1dx < 0 no caso indefinido e não-coercivo, sendo e1 a função associada ao primeiro valor próprio de + id em H1(R3) com peso h. Note-se que foi demonstrado que uma condi cão semelhante e condição necessária e suficiente na existência de solu cões positivas para equações elíticas semilineares com não-linearidades indefinidas em domínios limitados (ver e.g. Alama-Tarantello, Calc. Var. PDE 1 (1993), 439{475), ou ser uma condição suficiente na existência de soluções positivas para equações elíticas semilineares com não-linearidades indefinidas em RN (see e.g. Costa-Tehrani, Calc. Var. PDE 13 (2001), 159{189). Adicionalmente, o método utilizado pode ser utilizado para estudar outros aspetos dos sistemas de Schrodinger-Poisson, permite também estudar sistemas de Kirchho e sistemas de Schrodinger quasilineares. Por m, para obter soluções com mudança de sinal no Cap. 5, segue se a ideia de Hirano-Shioji, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), 333, mas o método utilizado é uma versão simplificada do método apresentado no artigo referido.
27
Feltrin, Guglielmo. "Positive solutions to indefinite problems: a topological approach." Doctoral thesis, SISSA, 2016. http://hdl.handle.net/20.500.11767/4933.
Повний текст джерелаАнотація:
The present Ph.D. thesis is devoted to the study of positive solutions to indefinite problems. In particular, we deal with the second order nonlinear differential equation u'' + a(t) g(u) = 0, where g : [0,+∞[→[0,+∞[ is a continuous nonlinearity and a : [0,T]→R is a Lebesgue integrable sign-changing weight. We analyze the Dirichlet, Neumann and periodic boundary value problems on [0,T] associated with the equation and we provide existence, nonexistence and multiplicity results for positive solutions. In the first part of the manuscript, we investigate nonlinearities g(u) with a superlinear growth at zero and at infinity (including the classical superlinear case g(u)=u^p, with p>1). In particular, we prove that there exist 2^m-1 positive solutions when a(t) has m positive humps separated by negative ones and the negative part of a(t) is sufficiently large. Then, for the Dirichlet problem, we solve a conjecture by Gómez‐Reñasco and López‐Gómez (JDE, 2000) and, for the periodic problem, we give a complete answer to a question raised by Butler (JDE, 1976). In the second part, we study the super-sublinear case (i.e. g(u) is superlinear at zero and sublinear at infinity). If a(t) has m positive humps separated by negative ones, we obtain the existence of 3^m-1 positive solutions of the boundary value problems associated with the parameter-dependent equation u'' + λ a(t) g(u) = 0, when both λ>0 and the negative part of a(t) are sufficiently large. We propose a new approach based on topological degree theory for locally compact operators on open possibly unbounded sets, which applies for Dirichlet, Neumann and periodic boundary conditions. As a byproduct of our method, we obtain infinitely many subharmonic solutions and globally defined positive solutions with complex behavior, and we deal with chaotic dynamics. Moreover, we study positive radially symmetric solutions to the Dirichlet and Neumann problems associated with elliptic PDEs on annular domains. Furthermore, this innovative technique has the potential and the generality needed to deal with indefinite problems with more general differential operators. Indeed, our approach apply also for the non-Hamiltonian equation u'' + cu' + a(t) g(u) = 0. Meanwhile, more general operators in the one-dimensional case and problems involving PDEs will be subjects of future investigations.
28
Piovano, Paulo. "Evolution and Regularity Results for Epitaxially Strained Thin Films and Material Voids." Research Showcase @ CMU, 2012. http://repository.cmu.edu/dissertations/96.
Повний текст джерелаАнотація:
In this dissertation we study free boundary problems that model the evolution of interfaces in the presence of elasticity, such as thin film profiles and material void boundaries. These problems are characterized by the competition between the elastic bulk energy and the anisotropic surface energy.
First, we consider the evolution equation with curvature regularization that models the motion of a two-dimensional thin film by evaporation-condensation on a rigid substrate. The film is strained due to the mismatch between the crystalline lattices of the two materials and anisotropy is taken into account. We present the results contained in [62] where the author establishes short time existence, uniqueness and regularity of the solution using De Giorgi’s minimizing movements to exploit the L2 -gradient flow structure of the equation. This seems to be the first analytical result for the evaporation-condensation case in the presence of elasticity.
Second, we consider the relaxed energy introduced in [20] that depends on admissible pairs (E, u) of sets E and functions u defined only outside of E. For dimension three this energy appears in the study of the material voids in solids, where the pairs (E, u) are interpreted as the admissible configurations that consist of void regions E in the space and of displacements u of the atoms of the crystal. We provide the precise mathematical framework that guarantees the existence of minimal energy pairs (E, u). Then, we establish that for every minimal configuration (E, u), the function u is C 1,γ loc -regular outside an essentially closed subset of E. No hypothesis of starshapedness is assumed on the voids and all the results that are contained in [18] hold true for every dimension d ≥ 2.
29
Palmieri, Alessandro [Verfasser], Michael [Akademischer Betreuer] Reissig, Michael [Gutachter] Reissig, and Vladimir [Gutachter] Georgiev. "Global in time existence and blow-up results for a semilinear wave equation with scale-invariant damping and mass / Alessandro Palmieri ; Gutachter: Michael Reissig, Vladimir Georgiev ; Betreuer: Michael Reissig." Freiberg : Technische Universität Bergakademie Freiberg, 2018. http://d-nb.info/1226100945/34.
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30
Al, Zohbi Maryam. "Contributions to the existence, uniqueness, and contraction of the solutions to some evolutionary partial differential equations." Thesis, Compiègne, 2021. http://www.theses.fr/2021COMP2646.
Повний текст джерелаАнотація:
Dans cette thèse, nous nous sommes principalement intéressés à l’étude théorique et numérique de quelques équations qui décrivent la dynamique des densités des dislocations. Les dislocations sont des défauts microscopiques qui se déplacent dans les matériaux sous l’effet des contraintes extérieures. Dans un premier travail, nous démontrons un résultat d’existence globale en temps des solutions discontinues pour un système hyperbolique diagonal qui n’est pas nécessairement strictement hyperbolique, dans un espace unidimensionnel. Ainsi dans un deuxième travail, nous élargissons notre portée en démontrant un résultat similaire pour un système d’équations de type eikonal non-linéaire qui est en fait une généralisation du système hyperbolique déjà étudié. En effet, nous prouvons aussi l’existence et l’unicité d’une solution continue pour le système eikonal. Ensuite, nous nous sommes intéressés à l’analyse numérique de ce système en proposant un schéma aux différences finies, par lequel nous montrons la convergence vers le problème continu et nous consolidons nos résultats avec quelques simulations numériques. Dans une autre direction, nous nous sommes intéressés à la théorie de contraction différentielle pour les équations d’évolutions. Après avoir introduit une nouvelle distance, nous construisons une nouvelle famille des solutions contractantes positives pour l’équation d’évolution p-LaplaceIn this thesis, we are mainly interested in the theoretical and numerical study of certain equations that describe the dynamics of dislocation densities. Dislocations are microscopic defects in materials, which move under the effect of an external stress. As a first work, we prove a global in time existence result of a discontinuous solution to a diagonal hyperbolic system, which is not necessarily strictly hyperbolic, in one space dimension. Then in another work, we broaden our scope by proving a similar result to a non-linear eikonal system, which is in fact a generalization of the hyperbolic system studied first. We also prove the existence and uniqueness of a continuous solution to the eikonal system. After that, we study this system numerically in a third work through proposing a finite difference scheme approximating it, of which we prove the convergence to the continuous problem, strengthening our outcomes with some numerical simulations. On a different direction, we were enthused by the theory of differential contraction to evolutionary equations. By introducing a new distance, we create a new family of contracting positive solutions to the evolutionary p-Laplacian equation
31
Dereudre, David, and Sylvie Roelly. "Path-dependent infinite-dimensional SDE with non-regular drift : an existence result." Universität Potsdam, 2014. http://opus.kobv.de/ubp/volltexte/2014/7208/.
Повний текст джерелаАнотація:
We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be neither small or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy. Our result strongly improves the previous ones obtained for free dynamics with a small perturbative drift. The originality of our method leads in the use of the
specific entropy as a tightness tool and on a description of such stochastic differential equation as solution of a variational problem on the path space.
32
McKinley, Scott Alister. "An existence result from the theory of fluctuating hydrodynamics of polymers in dilute solution." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1149020682.
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Orecchia, Giulio. "A monodromy criterion for existence of Néron models and a result on semi-factoriality." Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0017/document.
Повний текст джерелаАнотація:
Cette thèse est divisée en deux parties. Dans la première partie, nous introduisons une nouvelle condition, appelée additivité torique, sur une famille de variétés abéliennes qui dégénèrent en un schéma semi-abelien au-dessus d’un diviseur à croisements normaux. La condition ne dépend que du module de Tate T l A(K sep ) de la fibre générique. Nous montrons que l’additivité torique est une condition suffisante pour l’existence d’un modèle de Néron, si la base est un schéma de caractéristique nulle. Dans le cas de la jacobienne d’une courbe lisse à réduction semi-stable, on obtient le même résultat sans aucune hypothèse sur la caractéristique de base; et nous montrons que l’additivité torique est aussi nécessaire pour l’existence d’un modèle de Néron, si la base est un schéma de caractéristique nulle. Dans la deuxième partie, on considère le cas d’une famille de courbes nodales sur un anneau de valuation discrète. On donne une condition combinatoire sur le graphe dual de la fibre spéciale, appelée semi-factorialité, qui équivaut au fait que tous les faisceaux inversibles sur la fibre générique s’étendent en des faisceaux inversibles sur l’espace total de la courbe. Il est démontré par la suite que cette condition est automatiquement satisfaite après un éclatement centré aux points fermés non-réguliers de la famille de courbes. On applique le résultat ci-dessus pour généraliser un théorème de Raynaud sur le modèle de Néron des jacobiennes de courbes lisses, au cas des courbes nodalesThis thesis is subdivided in two parts. In the first part, we introduce a new condition, called toric-additivity, on a family of abelian varieties degenerating to a semi-abelian scheme over a normal crossing divisor. The condition depends only on the Tate module TlA(Ksep) of the generic fibre, for a prime l invertible on the base. We show that toric-additivity is a sufficient condition for the existence of a Néron model if the base is a Q-scheme. In the case of the jacobian of a smooth curve with semi-stable reduction, we obtain the same result without assumptions on the base characteristic; and we show that toric-additivity is also necessary for the existence of a Néron model, when the base is a Q-scheme. In the second part, we consider the case of a family of nodal curves over a discrete valuation ring, having split singularities. We say that such a family is semi factorial if every line bundle on the generic fibre extends to a line bundle on the total space. We give a necessary and sufficient condition for semi- factoriality, in terms of combinatorics of the dual graph of the special fibre. In particular, we show that performing one blow-up with center the non regular closed points yields a semi-factorial model of the generic fibre. As an application, we extend the result of Raynaud relating Néron models of smooth curves and Picard functors of their regular models to the case of nodal curves having a semi-factorial model
34
Roelly, Sylvie, and Pra Paolo Dai. "An existence result for infinite-dimensional Brownian diffusions with non- regular and non Markovian drift." Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2006/668/.
Повний текст джерелаАнотація:
We prove in this paper an existence result for infinite-dimensional stationary interactive Brownian diffusions. The interaction is supposed to be small in the norm ||.||∞ but otherwise is very general, being possibly non-regular and non-Markovian. Our method consists in using the characterization of such diffusions as space-time Gibbs fields so that we construct them by
space-time cluster expansions in the small coupling parameter.
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Ali, Zakaria Idriss. "Existence result for a class of stochastic quasilinear partial differential equations with non-standard growth." Diss., University of Pretoria, 2010. http://hdl.handle.net/2263/29519.
Повний текст джерелаАнотація:
In this dissertation, we investigate a very interesting class of quasi-linear stochastic partial differential equations. The main purpose of this article is to prove an existence result for such type of stochastic differential equations with non-standard growth conditions. The main difficulty in the present problem is that the existence cannot be easily retrieved from the well known results under Lipschitz type of growth conditions [42].Dissertation (MSc)--University of Pretoria, 2010.
Mathematics and Applied Mathematics
unrestricted
36
Moreno-Bromberg, Santiago. "Optimal design of over-the-counter derivatives in a principal-agent framework : an existence result and numerical implementations." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/5300.
Повний текст джерелаАнотація:
This work lies in the intersection of Mathematical Finance, Mathematical
Economics and Convex Analysis. In terms of the latter, a new result (to the
author’s knowledge) on a Lipschitz property of the derivatives of a convex
function is presented in the first chapter. An important result on its own,
it might also provide a stepping stone to an extension to Hubert spaces of
Alexandrov’s theorem on the second derivatives of convex functions.
The second chapter considers the problem of Adverse Selection and op
timal derivative design within a Principal-Agent framework. The principal’s
income is exposed to non-hedgeable risk factors arising, for instance, from
weather or climate phenomena. She evaluates her risk using a coherent and
law invariant risk measure and tries to minimize her exposure by selling
derivative securities on her income to individual agents. The agents have
mean-variance preferences with heterogeneous risk aversion coefficients. An
agent’s degree of risk aversion is private information and the principal only
knows their overall distribution. It is shown that the principal’s risk mini
mization problem has a solution and, in terms of the pricing schedule, the
latter is unique.
Finding a solution to the principal’s problem requires solving a varia
tional problem with global convexity constraints. In general, this cannot be
done in closed form. To this end an algorithm to approximate the solutions
to variational problems where set of admissible functions consists of convex
functions is presented in the fourth chapter of this work. Several examples
are provided.
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Franceschiello, Benedetta. "Mean curvature flow in SE (2) and applications to visual perception." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/6959/.
Повний текст джерелаАнотація:
Our goal in this thesis is to provide a result of existence of the degenerate non-linear, non-divergence PDE which describes the mean curvature flow in the Lie group SE(2) equipped with a sub-Riemannian metric. The research is motivated by problems of visual completion and models of the visual cortex.
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Kühn, Franziska. "Probability and Heat Kernel Estimates for Lévy(-Type) Processes." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-214839.
Повний текст джерелаАнотація:
In this thesis, we present a new existence result for Lévy-type processes. Lévy-type processes behave locally like a Lévy process, but the Lévy triplet may depend on the current position of the process. They can be characterized by their so-called symbol; this is the analogue of the characteristic exponent in the Lévy case. Using a parametrix construction, we prove the existence of Lévy-type processes with a given symbol under weak regularity assumptions on the regularity of the symbol. Applications range from existence results for stable-like processes and mixed processes to uniqueness results for Lévy-driven stochastic differential equations.
Moreover, we discuss sufficient conditions for the existence of moments of Lévy-type processes and derive estimates for fractional moments.
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ANSELLI, ANDREA. "PHI-CURVATURES, HARMONIC-EINSTEIN MANIFOLDS AND EINSTEIN-TYPE STRUCTURES." Doctoral thesis, Università degli Studi di Milano, 2020. http://hdl.handle.net/2434/703786.
Повний текст джерелаАнотація:
The aim of this thesis is to study the geometry of a Riemannian manifold M, with a special structure, called Einstein-type structure, depending on 3 real parameters, a smooth map phi into a target Riemannian manifold N, and a smooth function, called potential function, on M itself. We will occasionally let some of the parameters be smooth functions. The setting generalizes various previously studied situations:, Ricci solitons, almost Ricci-solitons, Ricci-harmonic solitons, quasi-Einstein manifolds and so on. By taking a constant potential function those structures reduces to harmonic-Einstein manifolds, that are a generalization of Einstein manifolds. The main ingredient of our analysis is the study of certain modified curvature tensors on M related to the map phi, called phi-curvatures, obtaining, for instance, their transformation laws under a conformal change of metric, and to develop a series of results for harmonic-Einstein manifolds that parallel those obtained for Einstein manifolds some times ago and also in the very recent literature. Einstein-type structures may be obtained, for some special values of the parameters involved, by a conformal deformation of a harmonic-Einstein manifold or even as the base of a warped product harmonic-Einstein manifold. The latter fact applies not only in the Riemannian but also in the Lorentzian setting and thus some Einstein-type structures are connected with solutions of the Einstein field equations, which are of particular interest in General Relativity. The main result of the thesis is the locally characterization, via a couple of integrability conditions and mild assumptions on the potential function, of Einstein-type structures with vanishing phi-Bach curvature (in the direction of the potential) as a warped product with harmonic-Einstein base and with an open real interval as fibre, extending in a very non trivial way a recent result for Bach flat Ricci solitons. Moreover the map phi depends only on the base of the warped product and not on the fibre . We also consider rigidity, triviality and non-existence results, both in the compact and non-compact cases. This is done via integral formulas and, in the non-compact case, via analytical tools, like the weak maximum principle and the classical results of Obata, Tashiro, Kanai.
40
Bourdin, Loïc. "Contributions au calcul des variations et au principe du maximum de Pontryagin en calculs time scale et fractionnaire." Thesis, Pau, 2013. http://www.theses.fr/2013PAUU3009/document.
Повний текст джерелаАнотація:
Cette thèse est une contribution au calcul des variations et à la théorie du contrôle optimal dans les cadres discret, plus généralement time scale, et fractionnaire. Ces deux domaines ont récemment connu un développement considérable dû pour l’un à son application en informatique et pour l’autre à son essor dans des problèmes physiques de diffusion anormale. Que ce soit dans le cadre time scale ou dans le cadre fractionnaire, nos objectifs sont de : a) développer un calcul des variations et étendre quelques résultats classiques (voir plus bas); b) établir un principe du maximum de Pontryagin (PMP en abrégé) pour des problèmes de contrôle optimal. Dans ce but, nous généralisons plusieurs méthodes variationnelles usuelles, allant du simple calcul des variations au principe variationnel d’Ekeland (couplé avec la technique des variations-aiguilles), en passant par l’étude d’invariances variationnelles par des groupes de transformations. Les démonstrations des PMPs nous amènent également à employer des théorèmes de point fixe et à prendre en considération la technique des multiplicateurs de Lagrange ou encore une méthode basée sur un théorème d’inversion locale conique. Ce manuscrit est donc composé de deux parties : la Partie 1 traite de problèmes variationnels posés sur time scale et la Partie 2 est consacrée à leurs pendants fractionnaires. Dans chacune de ces deux parties, nous suivons l’organisation suivante : 1. détermination de l’équation d’Euler-Lagrange caractérisant les points critiques d’une fonctionnelle Lagrangienne ; 2. énoncé d’un théorème de type Noether assurant l’existence d’une constante de mouvement pour les équations d’Euler-Lagrange admettant une symétrie ; 3. énoncé d’un théorème de type Tonelli assurant l’existence d’un minimiseur pour une fonctionnelle Lagrangienne et donc, par la même occasion, d’une solution pour l’équation d’Euler-Lagrange associée (uniquement en Partie 2) ; 4. énoncé d’un PMP (version forte en Partie 1, version faible en Partie 2) donnant une condition nécessaire pour les trajectoires qui sont solutions de problèmes de contrôle optimal généraux non-linéaires ; 5. détermination d’une condition de type Helmholtz caractérisant les équations provenant d’un calcul des variations (uniquement en Partie 1 et uniquement dans les cas purement continu et purement discret). Des théorèmes de type Cauchy-Lipschitz nécessaires à l’étude de problèmes de contrôle optimal sont démontrés en AnnexeThis dissertation deals with the mathematical fields called calculus of variations and optimal control theory. More precisely, we develop some aspects of these two domains in discrete, more generally time scale, and fractional frameworks. Indeed, these two settings have recently experience a significant development due to its applications in computing for the first one and to its emergence in physical contexts of anomalous diffusion for the second one. In both frameworks, our goals are: a) to develop a calculus of variations and extend some classical results (see below); b) to state a Pontryagin maximum principle (denoted in short PMP) for optimal control problems. Towards these purposes, we generalize several classical variational methods, including the Ekeland’s variational principle (combined with needle-like variations) as well as variational invariances via the action of groups of transformations. Furthermore, the investigations for PMPs lead us to use fixed point theorems and to consider the Lagrange multiplier technique and a method based on a conic implicit function theorem. This manuscript is made up of two parts : Part A deals with variational problems on time scale and Part B is devoted to their fractional analogues. In each of these parts, we follow (with minor differences) the following organization: 1. obtaining of an Euler-Lagrange equation characterizing the critical points of a Lagrangian functional; 2. statement of a Noether-type theorem ensuring the existence of a constant of motion for Euler-Lagrange equations admitting a symmetry;3. statement of a Tonelli-type theorem ensuring the existence of a minimizer for a Lagrangian functional and, consequently, of a solution for the corresponding Euler-Lagrange equation (only in Part B); 4. statement of a PMP (strong version in Part A and weak version in Part B) giving a necessary condition for the solutions of general nonlinear optimal control problems; 5. obtaining of a Helmholtz condition characterizing the equations deriving from a calculus of variations (only in Part A and only in the purely continuous and purely discrete cases). Some Picard-Lindelöf type theorems necessary for the analysis of optimal control problems are obtained in Appendices
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Tavares, Lucas Alves. "O envolvimento da proteína adaptadora 1 (AP-1) no mecanismo de regulação negativa do receptor CD4 por Nef de HIV-1." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/17/17136/tde-06012017-113215/.
Повний текст джерелаАнотація:
O Vírus da Imunodeficiência Humana (HIV) é o agente etiológico da Síndrome da Imunodeficiência Adquirida (AIDS). A AIDS é uma doença de distribuição mundial, e estima-se que existam atualmente pelo menos 36,9 milhões de pessoas infectadas com o vírus. Durante o seu ciclo replicativo, o HIV promove diversas alterações na fisiologia da célula hospedeira a fim de promover sua sobrevivência e potencializar a replicação. A rápida progressão da infecção pelo HIV-1 em humanos e em modelos animais está intimamente ligada à função da proteína acessória Nef. Dentre as diversas ações de Nef está a regulação negativa de proteínas importantes na resposta imunológica, como o receptor CD4. Sabe-se que esta ação resulta da indução da degradação de CD4 em lisossomos, mas os mecanismos moleculares envolvidos ainda são totalmente elucidados. Nef forma um complexo tripartite com a cauda citosólica de CD4 e a proteína adaptadora 2 (AP-2), em vesículas revestidas por clatrina nascentes, induzindo a internalização e degradação lisossomal de CD4. Pesquisas anteriores demonstraram que o direcionamento de CD4 aos lisossomos por Nef envolve a entrada do receptor na via dos corpos multivesiculares (MVBs), por um mecanismo atípico, pois, embora não necessite da ubiquitinação de carga, depende da ação de proteínas que compõem os ESCRTs (Endosomal Sorting Complexes Required for Transport) e da ação de Alix, uma proteína acessória da maquinaria ESCRT. Já foi reportado que Nef interage com subunidades dos complexos AP-1, AP-2, AP-3 e Nef não parece interagir com subunidades de AP-4 e AP-5. Entretanto, o papel da interação de Nef com AP-1 e AP-3 na regulação negativa de CD4 ainda não está totalmente elucidado. Ademais, AP-1, AP-2 e AP-3 são potencialmente heterogêneos devido à existência de isoformas múltiplas das subunidades codificadas por diferentes genes. Todavia, existem poucos estudos para demonstrar se as diferentes combinações de isoformas dos APs são formadas e se possuem propriedades funcionais distintas. O presente trabalho procurou identificar e caracterizar fatores celulares envolvidos na regulação do tráfego intracelular de proteínas no processo de regulação negativa de CD4 induzido por Nef. Mais especificamente, este estudo buscou caracterizar a participação do complexo AP-1 na modulação negativa de CD4 por Nef de HIV-1, através do estudo funcional das duas isoformas de ?-adaptina, subunidades de AP-1. Utilizando a técnica de Pull-down demonstramos que Nef é capaz de interagir com ?2. Além disso, nossos dados de Imunoblot indicaram que a proteína ?2-adaptina, e não ?1-adaptina, é necessária no processo de degradação lisossomal de CD4 por Nef e que esta participação é conservada para degradação de CD4 por Nef de diferentes cepas virais. Ademais, por citometria de fluxo, o silenciamento de ?2, e não de ?1, compromete a diminuição dos níveis de CD4 por Nef da membrana plasmática. A análise por imunofluorêsncia indireta também revelou que a diminuição dos níveis de ?2 impede a redistribuição de CD4 por Nef para regiões perinucleares, acarretando no acúmulo de CD4, retirados por Nef da membrana plasmática, em endossomos primários. A depleção de ?1A, outra subunidade de AP-1, acarretou na diminuição dos níveis celulares de ?2 e ?1, bem como, no comprometimento da eficiente degradação de CD4 por Nef. Além disso, foi possível observar que, ao perturbar a maquinaria ESCRT via super-expressão de HRS (uma subunidade do complexo ESCRT-0), ocorreu um acumulo de ?2 em endossomos dilatados contendo HRS-GFP, nos quais também detectou-se CD4 que foi internalizado por Nef. Em conjunto, os resultados indicam que ?2-adaptina é uma importante molécula para o direcionamento de CD4 por Nef para a via ESCRT/MVB, mostrando ser uma proteína relevante no sistema endo-lisossomal. Ademais, os resultados indicaram que as isoformas ?-adaptinas não só possuem funções distintas, mas também parecem compor complexos AP-1 com diferentes funções celulares, já que apenas a variante AP-1 contendo ?2, mas não ?1, participa da regulação negativa de CD4 por Nef. Estes estudos contribuem para o melhor entendimento dos mecanismos moleculares envolvidos na atividade de Nef, que poderão também ajudar na melhor compreensão da patogênese do HIV e da síndrome relacionada. Em adição, este trabalho contribui para o entendimento de processos fundamentais da regulação do tráfego de proteínas transmembrana no sistema endo-lisossomal.The Human Immunodeficiency Virus (HIV) is the etiologic agent of Acquired Immunodeficiency Syndrome (AIDS). AIDS is a disease which has a global distribution, and it is estimated that there are currently at least 36.9 million people infected with the virus. During the replication cycle, HIV promotes several changes in the physiology of the host cell to promote their survival and enhance replication. The fast progression of HIV-1 in humans and animal models is closely linked to the function of an accessory protein Nef. Among several actions of Nef, one is the most important is the down-regulation of proteins from the immune response, such as the CD4 receptor. It is known that this action causes CD4 degradation in lysosome, but the molecular mechanisms are still incompletely understood. Nef forms a tripartite complex with the cytosolic tail of the CD4 and adapter protein 2 (AP-2) in clathrin-coated vesicles, inducing CD4 internalization and lysosome degradation. Previous research has demonstrated that CD4 target to lysosomes by Nef involves targeting of this receptor to multivesicular bodies (MVBs) pathway by an atypical mechanism because, although not need charging ubiquitination, depends on the proteins from ESCRTs (Endosomal Sorting Complexes Required for Transport) machinery and the action of Alix, an accessory protein ESCRT machinery. It has been reported that Nef interacts with subunits of AP- 1, AP-2, AP-3 complexes and Nef does not appear to interact with AP-4 and AP-5 subunits. However, the role of Nef interaction with AP-1 or AP-3 in CD4 down-regulation is poorly understood. Furthermore, AP-1, AP-2 and AP-3 are potentially heterogeneous due to the existence of multiple subunits isoforms encoded by different genes. However, there are few studies to demonstrate if the different combinations of APs isoforms are form and if they have distinct functional properties. This study aim to identify and characterize cellular factors involved on CD4 down-modulation induced by Nef from HIV-1. More specifically, this study aimed to characterize the involvement of AP-1 complex in the down-regulation of CD4 by Nef HIV-1 through the functional study of the two isoforms of ?-adaptins, AP-1 subunits. By pull-down technique, we showed that Nef is able to interact with ?2. In addition, our data from immunoblots indicated that ?2- adaptin, not ?1-adaptin, is required in Nef-mediated targeting of CD4 to lysosomes and the ?2 participation in this process is conserved by Nef from different viral strains. Furthermore, by flow cytometry assay, ?2 depletion, but not ?1 depletion, compromises the reduction of surface CD4 levels induced by Nef. Immunofluorescence microscopy analysis also revealed that ?2 depletion impairs the redistribution of CD4 by Nef to juxtanuclear region, resulting in CD4 accumulation in primary endosomes. Knockdown of ?1A, another subunit of AP-1, resulted in decreased cellular levels of ?1 and ?2 and, compromising the efficient CD4 degradation by Nef. Moreover, upon artificially stabilizing ESCRT-I in early endosomes, via overexpression of HRS, internalized CD4 accumulates in enlarged HRS-GFP positive endosomes, where co-localize with ?2. Together, the results indicate that ?2-adaptin is a molecule that is essential for CD4 targeting by Nef to ESCRT/MVB pathway, being an important protein in the endo-lysosomal system. Furthermore, the results indicate that ?-adaptins isoforms not only have different functions, but also seem to compose AP-1 complex with distinct cell functions, and only the AP-1 variant comprising ?2, but not ?1, acts in the CD4 down-regulation induced by Nef. These studies contribute to a better understanding on the molecular mechanisms involved in Nef activities, which may also help to improve the understanding of the HIV pathogenesis and the related syndrome. In addition, this work contributes with the understanding of primordial process regulation on intracellular trafficking of transmembrane proteins.
42
Chan, Justin. "Asymptotic existence results on specific graph decompositions." Thesis, 2010. http://hdl.handle.net/1828/2909.
Повний текст джерелаАнотація:
This work examines various asymptotic edge-decomposition problems on graphs. A G-group divisible design (G-GDD) of type [g_1, ..., g_u] and index lambda is a decomposition of the edges of the complete lambda-fold multipartite graph H, with groups (maximal independent sets) G_1, ..., G_n, |G_i| = g_i, into graphs (blocks) isomorphic to G. We shall also examine special types of G-GDDs (such as G-frames) and prove that, given all parameters except u, these structures exist for all asymptotically large u satisfying the necessary conditions. Our primary technique is to invoke a useful theorem of Lamken and Wilson on edge-colored
graph decompositions. The basic construction for k-RGDDs shall be outlined at the end of the thesis.
43
Mou, Libin H. "Some existence and uniqueness results of harmonic maps." Thesis, 1990. http://hdl.handle.net/1911/16374.
Повний текст джерелаАнотація:
This thesis discusses some existence and uniqueness problems of harmonic maps. It consists of two parts: Part I. Existence of harmonic maps with prescribed finite singularities. Here we address the question of existence of a harmonic map from a spatial domain to the sphere S$\sp2$ which has a prescribed finite set of singularities.
Part II. Uniqueness of energy minimizing harmonic maps for almost all smooth boundary data. Suppose $\Omega$ is a smooth domain in R$\sp{m}$ and N is a compact smooth manifold. Here we show roughly that almost all smooth maps from $\partial\Omega$ to N serve as boundary values for a unique energy minimizing map u from $\Omega$ to N. This involves constructing a finite measure on a suitable (infinite dimensional) space of smooth boundary values.
44
Xu, Jia-Ren, and 許嘉仁. "Existence results of capillary surfaces over convex domains." Thesis, 1989. http://ndltd.ncl.edu.tw/handle/47886333637563213405.
Повний текст джерела
45
Baldelli, Laura. "Existence and multiplicity results for nonlinear elliptic problems." Doctoral thesis, 2022. http://hdl.handle.net/2158/1261959.
Повний текст джерелаАнотація:
In this work of thesis, we investigate existence and multiplicity results for
a class of nonlinear elliptic problems. First, we deal with problems involving
the p-Laplacian operator on bounded smooth domains, where a diffusion term
appears into the nonlinearity. For this reason, variational methods cannot be
used. Secondly, we treat existence and multiplicity of weak solutions for (p; q)-
Laplacian equations, as well as for singular p-Laplacian Schrodinger equations, in
the entire R^N whose nonlinearity combines a power-type term at critical level with
a subcritical term, involving also nontrivial weights and a positive parameter.
This latter case, considered also in a symmetric setting, allows us to use variational
methods, but in the delicate situation of lack of compactness, so that classical
results cannot be directly used, they need to be adapted.
46
"Ergodic control of multidimensional diffusions I. : the existence results." Laboratory for Information and Decision Systems, Massachusetts Institute of Technology], 1986. http://hdl.handle.net/1721.1/2951.
Повний текст джерела
47
謝宗憲. "Some existence results for soluations of traveling wave type." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/31120718744331384489.
Повний текст джерела
48
Chen, Show-Ching, and 陳秀青. "EXISTENCE RESULTS FOR HAMMERSTEIN INTEGRAL EQUATIONS AND RELATED TOPICS." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/99734197373023885880.
Повний текст джерелаАнотація:
碩士國立台北師範學院
數理教育研究所
90
Abstract We shall provide conditions on non-positive function f (t, u), the Hammerstein integral equation and the weighted Hammerstein integral equation have at least one solution.
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Della, Pietra Francesco. "Existence results for some classes of nonlinear elliptic problems." Tesi di dottorato, 2008. http://www.fedoa.unina.it/2014/1/Della_Pietra_Scienze_Matematiche.pdf.
Повний текст джерела
50
Lin, Ya-Ping, and 林雅萍. "Some existence results for steady states of reaction-diffusion systems." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/93457131788327469250.
Повний текст джерелаАнотація:
博士國立彰化師範大學
數學系所
94
Abstract In this thesis, we are interested in the existence of steady states of reaction-di.usion systems with skew-gradient structure. We use two di.erent types of variational arguments to study the existence of steady states. In addition, we obtain a standing wave solution, by making use of ordered methods for quasi-monotone systems.