Existence of solution to a critical equation with variable exponent [PDF]
, 2012 In this paper we study the existence problem for the $p(x)-$Laplacian operator with a nonlinear critical source. We find a local condition on the exponents ensuring the existence of a nontrivial solution that shows that the Pohozaev obstruction does not ...
Bonder, Julián Fernández +2 more
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Mountain pass theorems for non-differentiable functions and applications [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1993 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vicenţiu D. Rădulescu
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GENERAL QUASILINEAR PROBLEMS INVOLVING \(p(x)\)-LAPLACIAN WITH ROBIN BOUNDARY CONDITION
Ural Mathematical Journal, 2020 This paper deals with the existence and multiplicity of solutions for a class of quasilinear problems involving \(p(x)\)-Laplace type equation, namely $$ \left\{\begin{array}{lll} -\mathrm{div}\, (a(| \nabla u|^{p(x)})| \nabla u|^{p(x)-2} \nabla u ...
Hassan Belaouidel +2 more
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On a nonlinear eigenvalue problem in Sobolev spaces with variable exponent [PDF]
, 2005 We consider a class of nonlinear Dirichlet problems involving the $p(x)$--Laplace operator. Our framework is based on the theory of Sobolev spaces with variable exponent and we establish the existence of a weak solution in such a space.
Dinu, Teodora Liliana
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Existence and multiplications of solutions for a class of equation with a non-smooth potential [PDF]
Journal of Hyperstructures, 2015 This paper deals with the existence and multiplicity of solutions for a class of nonlocal p−Kirchhoff problem. Using the mountain pass theorem and fountain theorem, we establish the existence of at least one solution and infinitely many solutions for a ...
Fariba Fattahi, M. Alimohammady
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The structure of the critical set in the mountain-pass theorem for nondifferentiable functions [PDF]
Differential and Integral Equations, 2003 The paper studies the structure of the critical set at the level given by the minimax value in the mountain pass theorem for nonsmooth functionals expressed as a sum of a locally Lipschitz function and a proper, convex, lower semicontinuous function on a Banach space.
Giuseppina Barletta, S. Marano
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Schrödinger-Poisson system without growth and the Ambrosetti-Rabinowitz conditions
AIMS Mathematics, 2020 We consider the following Schrödinger-Poisson system $$\left\{ \begin{array}{l}{\rm{ - }}\Delta u + V\left(x \right)u + \phi u = \lambda f\left(u \right)\; \; \; \; \; {\rm{in}}\; {\mathbb{R}^3}, \\ - \Delta \phi = {u^2}, \mathop {\lim }\limits_{|x| \to +
Chen Huang, Gao Jia
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Abstract and Applied Analysis, 2014 This paper is concerned with the existence and multiplicity of fast homoclinic solutions for a class of damped vibration problems with impulsive effects.
Qiongfen Zhang
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Applying the mountain pass theorem to an asymptotically linear elliptic equation on RN
, 1999 C. A. Stuart, Huan‐Song Zhou
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Mountain pass type solutions for a nonlacal fractional a(.)-Kirchhoff type problems
Journal of Nonlinear Functional Analysis, 2021 . In this paper, we investigate the existence of a weak solution of a fractional Kirchhoff type problem driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space with homogeneous Dirichlet boundary conditions.
A. Benkirane, M. Srati
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