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1
Fiscella, A. "VARIATIONAL PROBLEMS INVOLVING NON-LOCAL ELLIPTIC OPERATORS." Doctoral thesis, Università degli Studi di Milano, 2014. http://hdl.handle.net/2434/245334.
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My thesis deals with nonlinear elliptic problems involving a non-local integrodifferential operator of fractional type. Our main results concern the existence of weak solutions for these problems and they are obtained using variational and topological methods.
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Maad, Sara. "Critical point theory with applications to semilinear problems without compactness." Doctoral thesis, Uppsala : Matematiska institutionen, Univ. [distributör], 2002. http://publications.uu.se/theses/91-506-1557-2/.
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König, Tobias [Verfasser], and Rupert [Akademischer Betreuer] Frank. "Symmetry, uniqueness and blow-up in some elliptic variational problems with critical exponent / Tobias König ; Betreuer: Rupert Frank." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2020. http://d-nb.info/1215499914/34.
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Souza, Diego Ferraz de. "Concentration-compactness principle and applications to nonlocal elliptic problems." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/9308.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The main goal of this work is to analyze concentration-compactness principles for fractional Sobolev spaces based on the concentration compactness principle of P.-L. Lions and in the pro le decomposition for weak convergence in Hilbert spaces due to K. Tintarev and K.-H Fieseler. As application, we address questions on compactness of the associated energy functional to the following nonlocal elliptic problems, $' ''''''&' ''''''% p qsu fpx; uq in RN; p qsu apxqu fpx; uq in RN; $&% p qsu V pxqu Kpxq u fpx; uq gpx; uq in R3; p q Kpxqu2 in R3; where 0 s 1; 0 1; 2 4s ¥ 3; ¡ 0 and Kpxq ¥ 0 belongs to a suitable Lebesgue space. We obtain existence results for a wide class of possible singular potentials apxq; not necessarily bounded away from zero and for oscillatory nonlinearities in both subcritical and critical growth range that may not satisfy the Ambrosetti-Rabinowitz condition.
O objetivo principal deste trabalho é analisar princípios de concentração de compacidade para espaços de Sobolev fracionários baseados na concentração de compacidade de P.-L. Lions e no per l de decomposição para convergência fraca em espaços de Hilbert devido a K. Tintarev e K.-H Fieseler. Como aplicação, abordamos questões sobre a compacidade do funcional energia associado aos seguintes problems elípticos não locais, $' ''''''&' ''''''% p qsu fpx; uq em RN; p qsu apxqu fpx; uq em RN; $&% p qsu V pxqu Kpxq u fpx; uq gpx; uq em R3; p q Kpxqu2 em R3; onde 0 s 1; 0 1; 2 4s ¥ 3; ¡ 0 e Kpxq ¥ 0 pertence a um espaço de Lebesgue adequado. Obtemos resultados de existência para uma vasta classe de potenciais apxq possivelmente singulares, não necessariamente limitados por baixo por uma constante positiva e para não linearidades oscilatórias em ambos os crescimentos subcríticos e críticos que podem não satisfazer a condição de Ambrosetti-Rabinowitz.
5
Freitas, Luciana Roze de. "Existência e multiplicidade de soluções para uma classe de problemas quasilineares com crescimento crítico exponencial." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-18012011-145302/.
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Neste trabalho, mostramos a existência e multiplicidade de soluções para a seguinte classe de equações elípticas quasilineares { - \'DELTA IND. \'NÜ\' POT. \'upsilon\' + \'|\'upsilon\'| POT. \'NÜ\' - 2 \'upsilon\' = f(x, u), \'upsilon\' \'DIFERENTE\' 0, \'upsilon\' \'PERTENCE A >>: Nu + jujN2 u = f(x; u); x 2 ; u 6= 0; u 2 W1;N( ); onde e um domnio em RN, N 2, N e o operador N-Laplaciano e f e uma func~ao que possui um crescimento crtico exponencial. Para obter nossos resultados utilizamos o Princpio Variacional de Ekeland, Teorema do Passo da Montanha, Categoria de Lusternik- Schnirelman, Ac~ao de Grupo e tecnicas baseadas na Teoria do G^enero. Palavras chaves: Problemas elpticos quasilineares, Metodo Variacional, N-Laplaciano, crescimento crtico exponencial, Princpio Variacional de Ekeland, Categoria de Lusternik- Schnirelman, Desigualdade de Trudinger-MoserIn this work, we show the existence and multiplicity of solutions for the following class of quasilinear elliptic equations { - \'DELTA\' IND. \'NÜ\' \'upsilon\'\' + |\'upsilon\'| POT. \'NÜ\' - 2 = f(x, \'upsilon\'), x \"IT BELONGS\' \'OMEGA\', \'upsilon\' \'DIFFERENT\' 0, \'upsilon\' \'IT BELONGS\' W POT. 1, \'NÜ\' ( OMEGA), where \'OMEGA\' is a domain in \' R POT. \'NÜ\' > OR = 2, \'DELTA\' IND. \'NÜ\' is the N-Laplacian operator and f is a function with exponential critical growth. To obtain our results we utilize the Ekeland Variational Principle, the Mountain Pass Theorem, Lusternik-Schnirelman of Category, Group Action and techniques based on Genus Theory
6
Guimarães, Angelo. "Existência e multiplicidade de soluções de problemas elípticos com termo semilinear côncavo-convexo." Universidade Federal de Goiás, 2017. http://repositorio.bc.ufg.br/tede/handle/tede/6901.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this work we study existence and multiplicity of weak solutions for the eliptic problem with semilinear concave convex term, in a limited domain of a N-dimensional euclidean space. If we take f=0 and σ=1 we have a problem homogeneous with critical Sobolev exponent in which we use the Mountain Pass Theorem to find existence of a solution when p
7
Milbers, Zoja. "Eigenvalue Problem for the 1-Laplace Operator." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2009. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1238150433158-43544.
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We consider the eigenvalue problem associated to the 1-Laplace operator. We define higher eigensolutions by means of weak slope and establish existence of a sequence of eigensolutions by using nonsmooth critical point theory. In addition, we deduce a new necessary condition for the first eigenvalue of the 1-Laplace operator by means of inner variationsWir betrachten das zum 1-Laplace-Operator gehörige Eigenwertproblem. Wir definieren höhere Eigenlösungen mittels weak slope und weisen die Existenz einer Folge von Eigenlösungen nach, indem wir die nichtglatte Theorie kritischer Punkte anwenden. Zusätzlich leiten wir eine neue notwendige Bedingung für den ersten Eigenwert des 1-Laplace-Operators mittels innerer Variationen her
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Abreu, Rafael dos Reis 1983. "Soluções ground state para algumas classes de problemas elípticos." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305901.
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Orientador: Marcelo da Silva MontenegroTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Neste trabalho, tratamos de resultados de existência de soluções ground state para algumas classes de problemas elípticos sobre espaços euclidianos ou sobre domínios exteriores. Nos casos em que consideramos um domínio exterior, consideramos a condição de fronteira de Dirichlet ou de Neumann. O fato de se considerar domínios não limitados naturalmente implica em algumas dificuldades como, por exemplo, a falta de compacidade. Quando isso ocorre, em geral, a condição Palais-Smale não é válida. Para contornar esta e outras dificuldades, usamos o Teorema do Passo da Montanha sem condição Palais-Smale, Lema de Lions e Teorema de Vitali. Em nosso estudo, utilizamos métodos variacionais explorando diversas técnicas para a obtenção de pontos críticos de funcionais associados a cada problema. Pontos críticos não nulos de cada funcional são soluções de seu respectivo problema
Abstract: In this work, we deal with existence of ground state solutions for some classes of elliptic problems on Euclidean spaces or on exterior domains. In cases where we consider an exterior domain, we consider the Dirichlet boundary condition or the Neumann boundary condition. Elliptic problems involving unbounded domains naturally have some difficulties, por example, the lack of compactness. When it occurs, in general, the Palais-Smale condition is not valid. To overcome this difficulty and others, we use the Mountain Pass Theorem without Palais-Smale condition, results due to Lions and the Vitali's Theorem. In our study, we use variational methods exploring techniques to obtain critical points of functionals related to each problem. Nonzero critical points of each functional are solutions of its respective problem
Doutorado
Matematica
Doutor em Matemática
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Almeida, Samuel Oliveira de. "Soluções para problemas elípticos envolvendo o expoente crítico de Sobolev." Universidade Federal de Juiz de Fora, 2013. https://repositorio.ufjf.br/jspui/handle/ufjf/1468.
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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Neste trabalho estudamos a existência de soluções para problemas elípticos envolvendo o expoente crítico de Sobolev. Primeiramente, investigamos a existência de soluções para um problema superlinear do tipo Ambrosetti-Prodi com ressonância em 1, onde 1 é o primeiro autovalor de (−Δ,1 0 (Ω)). Além disso, estudamos resultados de multiplicidade para uma classe de equações elípticas críticas relacionadas com o problema de Brézis-Nirenberg, com condição de contorno de Neumann sobre a bola.
In this work we study the existence of solutions for elliptic problems involving critical Sobolev exponent. Firstly we investigate the existence of solutions for an Ambrosetti-Prodi type superlinear problem with resonance at 1 , where 1 is the first eigenvalue of (−Δ,1 0 (Ω)). Besides, we study multiplicity results for a class of critical elliptic equations related to the Brézis-Nirenberg problem with Neumann boundary condition on a ball.
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Felix, Diego Dias. "Sobre uma classe de problemas elípticos envolvendo o crescimento do tipo Trudinger-Moser." Universidade Federal da Paraíba, 2015. http://tede.biblioteca.ufpb.br:8080/handle/tede/9263.
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Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq
In this work, we study a class of quasilinear elliptic problem involving nonlinearities with subcritical polynomial growth, subcritical exponential growth and critical exponential growth. Our main focus is to treat nonlinearities which do not satisfy the condition of super-quadratic of Ambrosetti-Rabinowitz. Our main tool is the Mountain Pass Theorem with the Cerami condition.
Neste trabalho, estudamos uma classe de problemas elípticos quase lineares envolvendo não linearidades com crescimento polinomial subcrítico, exponencial subcrítico e exponencial crítico. Nosso foco principal é tratar não linearidades que não satisfazem a condição de superquadraticidade de Ambrosetti-Rabinowitz. A nossa ferramenta é o Teorema do Passo da Montanha com a condição de Cerami.
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Sanyal, Sourav. "Predicting Critical Warps in Near-Threshold GPGPU Applications Using a Dynamic Choke Point Analysis." DigitalCommons@USU, 2019. https://digitalcommons.usu.edu/etd/7545.
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General purpose graphics processing units (GP-GPU), owing to their enormous thread-level parallelism, can significantly improve the power consumption at the near-threshold (NTC) operating region, while offering close to a super-threshold performance. However, process variation (PV) can drastically reduce the GPU performance at NTC. In this work, choke points—a unique device-level characteristic of PV at NTC—that can exacerbate the warp criticality problem in GPUs have been explored. It is shown that the modern warp schedulers cannot tackle the choke point induced critical warps in an NTC GPU. Additionally, Choke Point Aware Warp Speculator, a circuit-architectural solution is proposed to dynamically predict the critical warps in GPUs, and accelerate them in their respective execution units. The best scheme achieves an average improvement of ∼39% in performance, and ∼31% in energy-efficiency, over one state-of-the-art warp scheduler, across 15 GPGPU applications, while incurring marginal hardware overheads.
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Ferreira, Marcelo Carvalho. "Existência de soluções via métodos variacionais para uma classe de problemas quasilineares com expoentes variáveis." Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/7434.
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Previous issue date: 2014-02-22Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this thesis we establish existence and multiplicity results for solutions to some classes of problems on RN involving the p(x)-Laplacian operator. In the first part, we consider classes of problems dealing with nonlinearities possessing critical growth. Ultimately, we consider a class of problems with a nonlinearity possessing a subcritical growth. In this latter case, we searched for multi-bump solutions. Among the tools we used are Mountain Pass Theorem, Concentration-Compactness Principle, Lion s Lemma, Ekeland s Variational Principle and Penalization Method
Nesta tese estabelecemos resultados de existência e multiplicidade de soluções para algumas classes de problemas sobre RN envolvendo o operador p(x)-laplaciano. Na primeira parte, consideramos classes de problemas com não-linearidades tendo crescimento crítico. Na parte final, consideramos uma classe de problemas com não-linearidade tendo um crescimento subcrítico. Neste último caso, buscamos soluções do tipo multi-bump. Entre as ferramentas utilizadas estão o Teorema do Passo da Montanha, Príncipio de Concentração de Compacidade, Lema de Lions, Princípio Variacional de Ekeland e o Método de Penalização
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Pereira, Denilson da Silva. "Soluções nodais para problemas elípticos semilineares com crescimento crítico exponencial." Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/7449.
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Previous issue date: 2014-12-05Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
In this work, we study existence, non-existence and multiplicity results of nodal solutions for the nonlinear Schrödinger equation (P) -u + V (x)u = f(u) in ; where is a smooth domain in R2 which is not necessarily bounded, f is a continuous function which has exponential critical growth and V is a continuous and nonnegative potential. In the first part, we prove the existence of least energy nodal solution in both cases, bounded and unbounded domain. Moreover, we also prove a nonexistence result of least energy nodal solution for the autonomous case in whole R2. In the second part, we establish multiplicity of multi-bump type nodal solutions. Finally, for V - 0, we prove a result of infinitely many nodal solutions on a ball. The main tools used are Variational methods, Lions's Lemma, Penalization methods and a process of anti-symmetric continuation.
Neste trabalho, estudamos resultados de existência, não existência e multiplicidade de soluções nodais para a equação de Schrödinger não-linear (P) -u + V (x)u = f(u) em ;onde é um domínio suave em R2 não necessariamente limitado, f é uma função que possui crescimento crítico exponencial e V é um potencial contínuo e não-negativo. Na primeira parte, mostramos a existência de soluções nodais de energia mínima em ambos os casos, domínio limitado e ilimitado. Mostramos ainda um resultado de não existência de solução nodal de energia mínima para o caso autônomo em todo o R2. Na segunda parte, estabelecemos a multiplicidade de soluções do tipo multi-bump nodal. Finalmente, para V - 0, mostramos um resultado de existência de infinitas soluções nodais em uma bola. As principais ferramentas utilizadas são Métodos Variacionais, Lema de Deformação, Lema de Lions, Método de penalização e um processo de continuação anti-simétrica.
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Larsson, Kristoffer. "Kritiskt tänkande i samhällskunskap : En studie som ur ett fenomenografiskt perspektiv belyser manifesterat kritiskt tänkande bland elever i grundskolans år 9." Licentiate thesis, Karlstads universitet, Centrum för de samhällsvetenskapliga ämnenas didaktik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-6866.
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In this study a phenomenographic theoretical perspective is taken as departure for research on manifested critical thinking in civics among Swedish ninth-grade compulsory school students. According to the phenomenographic perspective students’ manifestations of critical thinking are linked to the way of experiencing the phenomena inducing a manifestation of critical thinking. Thus differences between students’ manifestations of critical thinking are linked to differences in the way of experiencing the phenomena inducing a manifestation of critical thinking. The empirical investigation in this study revolves around how 19 ninth-grade students experience four different tasks designed to induce manifestations of critical thinking. In broad terms the main aim of the study is to describe the students’ different ways of experiencing each specific task and furthermore, to link each specific way of experiencing a specific task to a specific type of manifested critical thinking in relation to that task. A more overarching aim is to offer and test the phenomenographic theoretical perspective as a way of conducting research on manifested critical thinking. The empirical results show how the way of experiencing a specific task plays a decisive roll for the type of manifested critical thinking, made possible in relation to the specific task. A more complex way of experiencing the task can be linked to a more complex manifestation of critical thinking in relation to the task. A less complex way of experiencing the task can be linked to a less complex manifestation of critical thinking in relation to the task. The study also suggests how these empirical results can be used in a pedagogical situation in order to enhance students manifested critical thinking in civics. Concerning the more overarching aim the study strongly points to a further use of the phenomenographic perspective when conducting research on students manifested critical thinking.
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Malavazi, Mazílio Coronel 1983. "Problemas elípticos do tipo côncavo-convexo com crescimento crítico e condição de Neumann." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307128.
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Orientador: Francisco Odair Vieira de PaivaTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: O resumo poderá ser visualizado no texto completo da tese digital
Abstract: The abstract is available with the full electronic document
Doutorado
Matematica
Doutor em Matemática
16
Littig, Samuel. "The Eigenvalue Problem of the 1-Laplace Operator." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-161044.
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As a first aspect the thesis treats existence results of the perturbed eigenvalue problem of the 1-Laplace operator. This is done with the aid of a quite general critical point theory results with the genus as topological index. Moreover we show that the eigenvalues of the perturbed 1-Laplace operator converge to the eigenvalues of the unperturebed 1-Laplace operator when the perturbation goes to zero. As a second aspect we treat the eigenvalue problems of the vectorial 1-Laplace operator and the symmetrized 1-Laplace operator. And as a third aspect certain related parabolic problems are considered.
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HEIDARKHANI, SHAPOUR. "Critical point approaches for second-order dynamic Sturm-Liouville boundary value problems." Doctoral thesis, 2021. http://hdl.handle.net/11570/3206600.
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Economics is a direction in which there becomes visible to be many
occasions for applications of time scales. The time scales approach will not
only unify the standard discrete and continuous models in economics, but also,
for example, authorizes for payments that reach unequally spaced points in
time. We are going to study dynamic optimization problems from economics,
construct a time scales model, and apply variational methods and critical
point theory to obtain the existence of solutions. We derive several conditions
ensuring existence of solutions of dynamic Sturm{Liouville boundary value
problems. Variational methods are utilized in the proofs. We discuss the
existence of at least one, three and in¯nitely many solutions for the problems
under di®erent conditions on the data. Examples are also given to illustrate
the main results.
18
Baldelli, Laura. "Existence and multiplicity results for nonlinear elliptic problems." Doctoral thesis, 2022. http://hdl.handle.net/2158/1261959.
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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.
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Littig, Samuel. "The Eigenvalue Problem of the 1-Laplace Operator: Local Perturbation Results and Investigation of Related Vectorial Questions." Doctoral thesis, 2014. https://tud.qucosa.de/id/qucosa%3A28551.
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As a first aspect the thesis treats existence results of the perturbed eigenvalue problem of the 1-Laplace operator. This is done with the aid of a quite general critical point theory results with the genus as topological index. Moreover we show that the eigenvalues of the perturbed 1-Laplace operator converge to the eigenvalues of the unperturebed 1-Laplace operator when the perturbation goes to zero. As a second aspect we treat the eigenvalue problems of the vectorial 1-Laplace operator and the symmetrized 1-Laplace operator. And as a third aspect certain related parabolic problems are considered.