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Journal articles on the topic 'Non-existence result'

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Published: 9 March 2023

Last updated: 10 March 2023

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1

Wu, Mingzhu, and Zuodong Yang. "Existence and Non-Existence Result for Singular Quasilinear Elliptic Equations." Applied Mathematics 01, no. 05 (2010): 351–56. http://dx.doi.org/10.4236/am.2010.15046.

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2

Diening, Lars, and Michael Růžička. "An existence result for non-Newtonian fluids in non-regular domains." Discrete & Continuous Dynamical Systems - S 3, no. 2 (2010): 255–68. http://dx.doi.org/10.3934/dcdss.2010.3.255.

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3

Paoli, Laetitia. "An existence result for non-smooth vibro-impact problems." Journal of Differential Equations 211, no. 2 (April 2005): 247–81. http://dx.doi.org/10.1016/j.jde.2004.11.008.

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4

Kachmar, Ayman, and Mikael Persson. "A non-existence result for the Ginzburg–Landau equations." Comptes Rendus Mathematique 347, no. 21-22 (November 2009): 1261–64. http://dx.doi.org/10.1016/j.crma.2009.09.024.

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5

Mustafa, M. T. "A non-existence result for compact Einstein warped products." Journal of Physics A: Mathematical and General 38, no. 47 (November 9, 2005): L791—L793. http://dx.doi.org/10.1088/0305-4470/38/47/l01.

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6

De Beule, J., A. Hallez, and L. Storme. "A non-existence result on Cameron–Liebler line classes." Journal of Combinatorial Designs 16, no. 4 (2008): 342–49. http://dx.doi.org/10.1002/jcd.20164.

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7

Trabucho, L. "Non-linear bone remodelling: an existence and uniqueness result." Mathematical Methods in the Applied Sciences 23, no. 15 (2000): 1331–46. http://dx.doi.org/10.1002/1099-1476(200010)23:15<1331::aid-mma168>3.0.co;2-y.

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8

Paronetto, Fabio. "An existence result for evolution equations in non-cylindrical domains." Nonlinear Differential Equations and Applications NoDEA 20, no. 6 (March 14, 2013): 1723–40. http://dx.doi.org/10.1007/s00030-013-0227-0.

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9

Harker, Patrick T. "Existence of competitive equilibria via Smith's non-linear complementarity result." Economics Letters 19, no. 1 (January 1985): 1–4. http://dx.doi.org/10.1016/0165-1765(85)90090-4.

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10

Chen, Sitong, Binlin Zhang, and Xianhua Tang. "Existence and non-existence results for Kirchhoff-type problems with convolution nonlinearity." Advances in Nonlinear Analysis 9, no. 1 (September 20, 2018): 148–67. http://dx.doi.org/10.1515/anona-2018-0147.

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Abstract This paper is concerned with the following Kirchhoff-type problem with convolution nonlinearity: -\bigg{(}a+b\int_{\mathbb{R}^{3}}\lvert\nabla u|^{2}\,\mathrm{d}x\bigg{)}% \Delta u+V(x)u=(I_{\alpha}*F(u))f(u),\quad x\in{\mathbb{R}}^{3},\,u\in H^{1}(% \mathbb{R}^{3}), where {a,b>0} , {I_{\alpha}\colon\mathbb{R}^{3}\rightarrow\mathbb{R}} , with {\alpha\in(0,3)} , is the Riesz potential, {V\in\mathcal{C}(\mathbb{R}^{3},[0,\infty))} , {f\in\mathcal{C}(\mathbb{R},\mathbb{R})} and {F(t)\kern-1.0pt=\kern-1.0pt\int_{0}^{t}f(s)\,\mathrm{d}s} . By using variational and some new analytical techniques, we prove that the above problem admits ground state solutions under mild assumptions on V and f. Moreover, we give a non-existence result. In particular, our results extend and improve the existing ones, and fill a gap in the case where {f(u)=|u|^{q-2}u} , with {q\in(1+\alpha/3,2]} .

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11

Carlotto, Alessandro, and Andrea Mondino. "A non-existence result for minimal catenoids in asymptotically flat spaces." Journal of the London Mathematical Society 95, no. 2 (January 9, 2017): 373–92. http://dx.doi.org/10.1112/jlms.12012.

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12

Allouba, Hassan. "A non-nonstandard proof of Reimers' existence result for heat SPDEs." Journal of Applied Mathematics and Stochastic Analysis 11, no. 1 (January 1, 1998): 29–41. http://dx.doi.org/10.1155/s1048953398000033.

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In 1989, Reimers gave a nonstandard proof of the existence of a solution to heat SPDEs, driven by space-time white noise, when the diffusion coefficient is continuous and satisfies a linear growth condition. Using the martingale problem approach, we give a non-nonstandard proof of this fact, and with the aid of Girsanov's theorem for continuous orthogonal martingale measures (proved in a separate paper by the author), the result is extended to the case of a measurable drift.

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13

Baranovskii, Evgenii S., Vyacheslav V. Provotorov, Mikhail A. Artemov, and Alexey P. Zhabko. "Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results." Symmetry 13, no. 7 (July 19, 2021): 1300. http://dx.doi.org/10.3390/sym13071300.

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This paper deals with a 3D mathematical model for the non-isothermal steady-state flow of an incompressible fluid with temperature-dependent viscosity in a pipeline network. Using the pressure and heat flux boundary conditions, as well as the conjugation conditions to satisfy the mass balance in interior junctions of the network, we propose the weak formulation of the nonlinear boundary value problem that arises in the framework of this model. The main result of our work is an existence theorem (in the class of weak solutions) for large data. The proof of this theorem is based on a combination of the Galerkin approximation scheme with one result from the field of topological degrees for odd mappings defined on symmetric domains.

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14

Goufo, Emile Franc Doungmo, Morgan Kamga Pene, and Jeanine N. Mwambakana. "Existence result and conservativeness for a fractional order non-autonomous fragmentation dynamics." Journal of Nonlinear Sciences and Applications 09, no. 11 (November 30, 2016): 5850–61. http://dx.doi.org/10.22436/jnsa.009.11.13.

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15

Bender, Christian, and Lauri Viitasaari. "A general non-existence result for linear BSDEs driven by Gaussian processes." Stochastic Processes and their Applications 127, no. 4 (April 2017): 1204–33. http://dx.doi.org/10.1016/j.spa.2016.07.012.

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16

Dereudre, David, and Sylvie Rœlly. "Path-dependent infinite-dimensional SDE with non-regular drift: An existence result." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 53, no. 2 (May 2017): 641–57. http://dx.doi.org/10.1214/15-aihp728.

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17

Anderson, C. H., and J. Prasad. "On the non-existence of some interpolatory polynomials." International Journal of Mathematics and Mathematical Sciences 9, no. 4 (1986): 753–56. http://dx.doi.org/10.1155/s016117128600090x.

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Here we prove that ifxk,k=1,2,…,n+2are the zeros of(1−x2)Tn(x)whereTn(x)is the Tchebycheff polynomial of first kind of degreen,αj,βj,j=1,2,…,n+2andγj,j=1,2,…,n+1are any real numbers there does not exist a unique polynomialQ3n+3(x)of degree≤3n+3satisfying the conditions:Q3n+3(xj)=αj,Q3n+3(xj)=βj,j=1,2,…,n+2andQ‴3n+3(xj)=γj,j=2,3,…,n+1. Similar result is also obtained by choosing the roots of(1−x2)Pn(x)as the nodes of interpolation wherePn(x)is the Legendre polynomial of degreen.

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18

Dos Santos, Mickaël, and Rémy Rodiac. "Existence and non-existence results for minimizers of the Ginzburg–Landau energy with prescribed degrees." Communications in Contemporary Mathematics 18, no. 05 (July 18, 2016): 1650017. http://dx.doi.org/10.1142/s0219199716500176.

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Let [Formula: see text] be a smooth annular type domain. We consider the simplified Ginzburg–Landau energy [Formula: see text], where [Formula: see text], and look for minimizers of [Formula: see text] with prescribed degrees [Formula: see text], [Formula: see text] on the boundaries of the domain. For large [Formula: see text] and for balanced degrees (i.e. [Formula: see text]), we obtain existence of minimizers for domains with large capacity (corresponding to thin annulus). We also prove non-existence of minimizers of [Formula: see text], for large [Formula: see text], if [Formula: see text], [Formula: see text] and if [Formula: see text] is a circular annulus with large capacity. Our approach relies on similar results obtained for the Dirichlet energy [Formula: see text], on a previous existence result obtained by Berlyand and Golovaty and on a technique developed by Misiats.

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19

Zeng, Biao. "Feedback control for non-stationary 3D Navier–Stokes–Voigt equations." Mathematics and Mechanics of Solids 25, no. 12 (June 12, 2020): 2210–21. http://dx.doi.org/10.1177/1081286520926557.

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The goal of this article is to study the feedback control for non-stationary three-dimensional Navier–Stokes–Voigt equations. Based on the existence, uniqueness, and boundedness result of the weak solutions to the equations, we obtain the existence of solutions to the feedback control system. An existence result for an optimal control problem is also given. We illustrate our main result with an evolutionary hemivariational inequality.

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20

Covei, Dragos-Patru. "Non-existence result for radially symmetric solutions to the Lane–Emden–Fowler equations." Nonlinear Analysis: Theory, Methods & Applications 70, no. 1 (January 2009): 563–66. http://dx.doi.org/10.1016/j.na.2007.12.013.

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21

Gravejat, Philippe. "A Non-Existence Result for Supersonic Travelling Waves in the Gross-Pitaevskii Equation." Communications in Mathematical Physics 243, no. 1 (November 1, 2003): 93–103. http://dx.doi.org/10.1007/s00220-003-0961-y.

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22

Petitta, Francesco. "A non-existence result for nonlinear parabolic equations with singular measures as data." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 139, no. 2 (March 25, 2009): 381–92. http://dx.doi.org/10.1017/s0308210507001163.

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In this paper we prove a non-existence result for nonlinear parabolic problems with zero lower-order terms whose model iswhere Δp=div(|∇u|p−2∇u) is the usual p-laplace operator, λ is measure concentrated on a set of zero parabolic r-capacity (1<p<r) and q is large enough.

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23

Buratti, Marco, and Gloria Rinaldi. "A non-existence result on cyclic cycle-decompositions of the cocktail party graph." Discrete Mathematics 309, no. 14 (July 2009): 4722–26. http://dx.doi.org/10.1016/j.disc.2008.05.042.

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24

Kummer, Martin, Richard C. Churchill, and David L. Rod. "On a Result of Bruns." Canadian Mathematical Bulletin 33, no. 2 (June 1, 1990): 175–80. http://dx.doi.org/10.4153/cmb-1990-029-9.

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AbstractBruns' Theorem states that the classical integrals of the gravitational three-body problem generate all algebraic integrals. We show that the first step in his proof, together with Ziglin's non-integrability criterion for complex systems, can be used to prove the non-existence of energy independent algebraic integrals in certain real analytic systems. We also show that this aspect of Bruns' argument is purely algebraic: We offer a proof based on elementary differential algebraic methods.

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25

Celada, P., and S. Perrotta. "Minimizing non-convex multiple integrals: a density result." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 130, no. 4 (August 2000): 721–41. http://dx.doi.org/10.1017/s030821050000038x.

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We consider variational problems of the form where Ω is a bounded open set in RN, f : RN → R is a possibly non-convex lower semicontinuous function with p-growth at infinity for some 1 < p < ∞, and the boundary datum u0 is any function in W1, p (Ω). Assuming that the convex envelope f** of f is affine on each connected component of the set {f** < f}, we prove the existence of solutions to ( P) for every continuous function g such that (i) g has no strict local minima and (ii) every convergent sequence of extremum points of g eventually belongs to an interval where g is constant, thus showing that the set of continuous functions g that yield existence to (P) is dense in the space of continuous functions on R.

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26

Ghinelli, Dina, and Dieter Jungnickel. "A Non-Existence Result For Finite Projective Planes In Lenz-Barlotti Class I.4." Combinatorica 27, no. 2 (March 2007): 163–66. http://dx.doi.org/10.1007/s00493-007-0049-y.

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27

Boukhsas, Abdelmajid, Abdellah Ahmed Zerouali, Omar Chakrone, and Belhadj Karim. "On a positive solutions for $(p,q)$-Laplacian Steklov problem with two parameters." Boletim da Sociedade Paranaense de Matemática 40 (January 30, 2022): 1–19. http://dx.doi.org/10.5269/bspm.46385.

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We study the existence and non-existence of positive solutions for $(p,q)$-Laplacian Steklov problem with two parameters. The main result of our research is the construction of a continuous curve in plane, which becomes a threshold between the existence and non-existence of positive solutions.

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28

Khademloo, Somayeh, and Shapur Heidarkhani. "Existence of non-negative solutions for semilinear elliptic systems via variational methods." Nonlinear Analysis: Modelling and Control 17, no. 2 (April 25, 2012): 194–209. http://dx.doi.org/10.15388/na.17.2.14068.

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In this paper we consider a semilinear elliptic system with nonlinearities, indefinite weight functions and critical growth terms in bounded domains. The existence result of nontrivial nonnegative solutions is obtained by variational methods.

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29

Lam, C. W. H., L. Thiel, and S. Swiercz. "The Non-Existence of Finite Projective Planes of Order 10." Canadian Journal of Mathematics 41, no. 6 (December 1, 1989): 1117–23. http://dx.doi.org/10.4153/cjm-1989-049-4.

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A finite projective plane of order n, with n > 0, is a collection of n2+ n + 1 lines and n2+ n + 1 points such that1. every line contains n + 1 points,2. every point is on n + 1 lines,3. any two distinct lines intersect at exactly one point, and4. any two distinct points lie on exactly one line.It is known that a plane of order n exists if n is a prime power. The first value of n which is not a prime power is 6. Tarry [18] proved in 1900 that a pair of orthogonal latin squares of order 6 does not exist, which by Bose's 1938 result [3] implies that a projective plane of order 6 does not exist.

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30

COSTANTINI, STEFANIA. "On the existence of stable models of non-stratified logic programs." Theory and Practice of Logic Programming 6, no. 1-2 (January 2006): 169–212. http://dx.doi.org/10.1017/s1471068405002589.

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In this paper we analyze the relationship between cyclic definitions and consistency in Gelfond-Lifschitz's answer sets semantics (originally defined as ‘stable model semantics’). This paper introduces a fundamental result, which is relevant for Answer Set programming, and planning. For the first time since the definition of the stable model semantics, the class of logic programs for which a stable model exists is given a syntactic characterization. This condition may have a practical importance both for defining new algorithms for checking consistency and computing answer sets, and for improving the existing systems. The approach of this paper is to introduce a new canonical form (to which any logic program can be reduced to), to focus the attention on cyclic dependencies. The technical result is then given in terms of programs in canonical form (canonical programs), without loss of generality: the stable models of any general logic program coincide (up to the language) to those of the corresponding canonical program. The result is based on identifying the cycles contained in the program, showing that stable models of the overall program are composed of stable models of suitable sub-programs, corresponding to the cycles, and on defining the Cycle Graph. Each vertex of this graph corresponds to one cycle, and each edge corresponds to one handle, which is a literal containing an atom that, occurring in both cycles, actually determines a connection between them. In fact, the truth value of the handle in the cycle where it appears as the head of a rule, influences the truth value of the atoms of the cycle(s) where it occurs in the body. We can therefore introduce the concept of a handle path, connecting different cycles. Cycles can be even, if they consist of an even number of rules, or vice versa they can be odd. Problems for consistency, as it is well-known, originate in the odd cycles. If for every odd cycle we can find a handle path with certain properties, then the existence of stable model is guaranteed. We will show that based on this results new classes of consistent programs can be defined, and that cycles and cycle graphs can be generalized to components and component graphs.

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31

FUHRMANN, GABRIEL. "Non-smooth saddle-node bifurcations I: existence of an SNA." Ergodic Theory and Dynamical Systems 36, no. 4 (December 2, 2014): 1130–55. http://dx.doi.org/10.1017/etds.2014.92.

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We study one-parameter families of quasi-periodically forced monotone interval maps and provide sufficient conditions for the existence of a parameter at which the respective system possesses a non-uniformly hyperbolic attractor. This is equivalent to the existence of a sink-source orbit, that is, an orbit with positive Lyapunov exponent both forwards and backwards in time. The attractor itself is a non-continuous invariant graph with negative Lyapunov exponent, often referred to as ‘SNA’. In contrast to former results in this direction, our conditions are${\mathcal{C}}^{2}$-open in the fibre maps. By applying a general result about saddle-node bifurcations in skew-products, we obtain a conclusion on the occurrence of non-smooth bifurcations in the respective families. Explicit examples show the applicability of the derived statements.

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32

Molica Bisci, Giovanni, and Raffaella Servadei. "A bifurcation result for non-local fractional equations." Analysis and Applications 13, no. 04 (April 28, 2015): 371–94. http://dx.doi.org/10.1142/s0219530514500067.

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In the present paper, we consider problems modeled by the following non-local fractional equation [Formula: see text] where s ∈ (0, 1) is fixed, (-Δ)sis the fractional Laplace operator, λ and μ are real parameters, Ω is an open bounded subset of ℝn, n > 2s, with Lipschitz boundary and f is a function satisfying suitable regularity and growth conditions. A critical point result for differentiable functionals is exploited, in order to prove that the problem admits at least one non-trivial and non-negative (non-positive) solution, provided the parameters λ and μ lie in a suitable range. The existence result obtained in the present paper may be seen as a bifurcation theorem, which extends some results, well known in the classical Laplace setting, to the non-local fractional framework.

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33

Pathak, Vijai Kumar, and Lakshmi Narayan Mishra. "Application of Fixed Point Theorem to Solvability for Non-Linear Fractional Hadamard Functional Integral Equations." Mathematics 10, no. 14 (July 8, 2022): 2400. http://dx.doi.org/10.3390/math10142400.

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In the present paper, our main work aims to discover the existence result of the fractional order non-linear Hadamard functional integral equations on [1,a] by employing the theory of measure of non-compactness together with the fixed point theory in Banach space. An example is presented to see the validity and practicability of our existence result.

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34

Biagi, Stefano, Alessandro Calamai, and Gennaro Infante. "Nonzero Positive Solutions of Elliptic Systems with Gradient Dependence and Functional BCs." Advanced Nonlinear Studies 20, no. 4 (November 1, 2020): 911–31. http://dx.doi.org/10.1515/ans-2020-2101.

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AbstractWe discuss, by topological methods, the solvability of systems of second-order elliptic differential equations subject to functional boundary conditions under the presence of gradient terms in the nonlinearities. We prove the existence of nonnegative solutions and provide a non-existence result. We present some examples to illustrate the applicability of the existence and non-existence results.

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35

Singh, Tej Bahadur. "Non-existence of odd periodic maps on certain spaces without fixed points." Bulletin of the Australian Mathematical Society 32, no. 3 (December 1985): 389–97. http://dx.doi.org/10.1017/s0004972700002501.

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In this paper, we show that the fixed point set of Zp-actions, p an odd prime, on a finitistic space X of type (a, b) is non-empty, whenever b ≡ 0 (mod p). We also prove a similar result for circle group actions of finitistic spaces of (a, 0) type.

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36

Mechai, Idir, Metib Alghamdi, and Habib Yazidi. "Existence of solutions of a non-variational bi-harmonic system via fixed point theory." Filomat 32, no. 12 (2018): 4113–30. http://dx.doi.org/10.2298/fil1812113m.

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We prove existence of a positive solution for a system of non-variational bi-harmonic equations. Furthermore, we give some a priori estimates of solutions and a non-existence result. In addition we compute numerical solutions to illustrate the theoretical results.

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37

Alkhayal, Jana, Samar Issa, Mustapha Jazar, and Régis Monneau. "Existence result for degenerate cross-diffusion system with application to seawater intrusion." ESAIM: Control, Optimisation and Calculus of Variations 24, no. 4 (October 2018): 1735–58. http://dx.doi.org/10.1051/cocv/2017058.

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In this paper we study a degenerate parabolic system, which is strongly coupled. We prove general existence result, but the uniqueness question remains open. Our proof of existence is based on a crucial entropy estimate which controls the gradient of the solution together with its non-negativity. Our system is of porous medium type which is applicable to models in seawater intrusion.

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38

TACHIKAWA, Atsushi. "A Non-Existence Result for Harmonic Mappings from $\mathbf{R}^n$ into $\mathbf{H}^n$." Tokyo Journal of Mathematics 11, no. 2 (December 1988): 311–16. http://dx.doi.org/10.3836/tjm/1270133976.

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39

Ma, Li, and Xingwang Xu. "Uniform bound and a non-existence result for Lichnerowicz equation in the whole n-space." Comptes Rendus Mathematique 347, no. 13-14 (July 2009): 805–8. http://dx.doi.org/10.1016/j.crma.2009.04.017.

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40

Muñoz-Vázquez, Aldo-Jonathan, Anand Sánchez-Orta, and Vicente Parra-Vega. "A general result on non-existence of finite-time stable equilibria in fractional-order systems." Journal of the Franklin Institute 356, no. 1 (January 2019): 268–75. http://dx.doi.org/10.1016/j.jfranklin.2018.11.001.

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41

Bazgir, Hamed, and Bahman Ghazanfari. "Existence of Solutions for Fractional Integro-Differential Equations with Non-Local Boundary Conditions." Mathematical and Computational Applications 23, no. 3 (July 14, 2018): 36. http://dx.doi.org/10.3390/mca23030036.

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In this paper, we study the existence of solutions for a new class of boundary value problems of non-linear fractional integro-differential equations. The existence result is obtained with the aid of Schauder type fixed point theorem while the uniqueness of solution is established by means of contraction mapping principle. Then, we present some examples to illustrate our results.

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42

Meraj, Arshi, and Dwijendra N. Pandey. "Existence of mild solutions for fractional non-instantaneous impulsive integro-differential equations with nonlocal conditions." Arab Journal of Mathematical Sciences 26, no. 1/2 (November 27, 2018): 3–13. http://dx.doi.org/10.1016/j.ajmsc.2018.11.002.

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This paper is concerned with the existence of mild solutions for a class of fractional semilinear integro-differential equations having non-instantaneous impulses. The result is obtained by using noncompact semigroup theory and fixed point theorem. The obtained result is illustrated by an example at the end.

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43

Di, Huafei, and Zefang Song. "Global existence and blow-up phenomenon for a quasilinear viscoelastic equation with strong damping and source terms." Opuscula Mathematica 42, no. 2 (2022): 119–55. http://dx.doi.org/10.7494/opmath.2022.42.2.119.

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Considered herein is the global existence and non-global existence of the initial-boundary value problem for a quasilinear viscoelastic equation with strong damping and source terms. Firstly, we introduce a family of potential wells and give the invariance of some sets, which are essential to derive the main results. Secondly, we establish the existence of global weak solutions under the low initial energy and critical initial energy by the combination of the Galerkin approximation and improved potential well method involving with \(t\). Thirdly, we obtain the finite time blow-up result for certain solutions with the non-positive initial energy and positive initial energy, and then give the upper bound for the blow-up time \(T^\ast\). Especially, the threshold result between global existence and non-global existence is given under some certain conditions. Finally, a lower bound for the life span \(T^\ast\) is derived by the means of integro-differential inequality techniques.

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44

Legendre, Eveline. "Existence and non-uniqueness of constant scalar curvature toric Sasaki metrics." Compositio Mathematica 147, no. 5 (July 27, 2011): 1613–34. http://dx.doi.org/10.1112/s0010437x1100529x.

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AbstractWe study compatible toric Sasaki metrics with constant scalar curvature on co-oriented compact toric contact manifolds of Reeb type of dimension at least five. These metrics come in rays of transversal homothety due to the possible rescaling of the Reeb vector fields. We prove that there exist Reeb vector fields for which the transversal Futaki invariant (restricted to the Lie algebra of the torus) vanishes. Using an existence result of E. Legendre [Toric geometry of convex quadrilaterals, J. Symplectic Geom. 9 (2011), 343–385], we show that a co-oriented compact toric contact 5-manifold whose moment cone has four facets admits a finite number of rays of transversal homothetic compatible toric Sasaki metrics with constant scalar curvature. We point out a family of well-known toric contact structures on S2×S3 admitting two non-isometric and non-transversally homothetic compatible toric Sasaki metrics with constant scalar curvature.

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45

Silvestre, Luis, and Stanley Snelson. "Solutions to the non-cutoff Boltzmann equation uniformly near a Maxwellian." Mathematics in Engineering 5, no. 2 (2022): 1–36. http://dx.doi.org/10.3934/mine.2023034.

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<abstract><p>The purpose of this paper is to show how the combination of the well-known results for convergence to equilibrium and conditional regularity, in addition to a short-time existence result, lead to a quick proof of the existence of global smooth solutions for the non cutoff Boltzmann equation when the initial data is close to equilibrium. We include a short-time existence result for polynomially-weighted $ L^\infty $ initial data. From this, we deduce that if the initial data is sufficiently close to a Maxwellian in this norm, then a smooth solution exists globally in time.</p></abstract>

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46

FONSECA, PEDRO D. "NON-EXISTENCE OF LOCAL INTEGRALS OF MOTION IN THE MULTI-DEFORMED ISING MODEL." Modern Physics Letters A 13, no. 24 (August 10, 1998): 1931–35. http://dx.doi.org/10.1142/s0217732398002047.

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We confirm the non-integrability of the multi-deformed Ising model — an already expected result. After deforming with the energy operator ϕ1,3, we use the Majorana free fermionic representation for the massive theory to show that, besides the trivial one, no local integrals of motion can be built in the theory arising from perturbing with both energy and spin operators.

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47

Bonanno, Gabriele, Giuseppina Barletta, and Donal O’Regan. "A variational approach to multiplicity results for boundary-value problems on the real line." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 145, no. 1 (January 30, 2015): 13–29. http://dx.doi.org/10.1017/s0308210513001200.

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We study the existence and multiplicity of solutions for a parametric equation driven by the p-Laplacian operator on unbounded intervals. Precisely, by using a recent local minimum theorem we prove the existence of a non-trivial non-negative solution to an equation on the real line, without assuming any asymptotic condition either at 0 or at ∞ on the nonlinear term. As a special case, we note the existence of a non-trivial solution for the problem when the nonlinear term is sublinear at 0. Moreover, under a suitable superlinear growth at ∞ on the nonlinearity we prove a multiplicity result for such a problem.

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del Pino, Manuel, Raúl Manásevich, and Alberto Montero. "T-periodic solutions for some second order differential equations with singularities." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 120, no. 3-4 (1992): 231–43. http://dx.doi.org/10.1017/s030821050003211x.

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SynopsisWe study the existence of T-periodic positive solutions of the equationwhere f(t, .) has a singularity of repulsive type near the origin. Under the assumption that f(t, x) lies between two lines of positive slope for large and positive x, we find a non-resonance condition which predicts the existence of one T-periodic solution.Our main result gives a Fredholm alternative-like result for the existence of T-periodic positive solutions for

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Ait Hammou, Mustapha, Elhoussine Azroul, and Badr Lahmi. "An existence result for a strongly nonlinear parabolic equations with variable nonlinearity." Proyecciones (Antofagasta) 41, no. 1 (February 1, 2022): 111–35. http://dx.doi.org/10.22199/issn.0717-6279-4457.

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We prove the existence of a solution for the strongly nonlinear parabolic initial boundary value problem associated to the equation ut − div a(x, t, ∇u) + g(x, t, u, ∇u) = f, where the vector field a(x, t, ξ) exhibits non-standard growth conditions.

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CHUNG, NGUYEN THANH, and QUỐC ANH NGÔ. "A MULTIPLICITY RESULT FOR A CLASS OF EQUATIONS OFp-LAPLACIAN TYPE WITH SIGN-CHANGING NONLINEARITIES." Glasgow Mathematical Journal 51, no. 3 (September 2009): 513–24. http://dx.doi.org/10.1017/s001708950900514x.

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AbstractUsing variational arguments we study the non-existence and multiplicity of non-negative solutions for a class equations of the formwhere Ω is a bounded domain inN,N≧ 3,fis a sign-changing Carathéodory function on Ω × [0, +∞) and λ is a positive parameter.

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