Results 21 to 30 of about 24,150 (220)
Multiple solutions for a quasilinear Choquard equation with critical nonlinearity
Open Mathematics, 2021 In the present work, we are concerned with the multiple solutions for quasilinear Choquard equation with critical nonlinearity in RN{{\mathbb{R}}}^{N}.
Li Rui, Song Yueqiang
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Journal of Differential Equations, 1985 In this paper we establish a new version of the well-known theorem of Ambrosetti and Rabinowitz on the existence of critical points for functionals \(I: X\to {\mathbb{R}}\) of class \(C^ 1\) on a real Banach space X. As usual, a compactness condition of Palais-Smale type is assumed throughout, including a version particularly suited to the periodic ...
PUCCI, Patrizia, J. SERRIN
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On p-Laplace Equations with Singular Nonlinearities and Critical Sobolev Exponent
Journal of Function Spaces, 2022 In this paper, we deal with p-Laplace equations with singular nonlinearities and critical Sobolev exponent. By using the Nehari manifold, Mountain Pass theorem, and Maximum principle theorem, we prove the existence of at least four distinct nontrivial ...
Mohammed El Mokhtar ould El Mokhtar
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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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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 $$ \left\{\begin{array}{lll} -\mathrm{div}\, (a(| \nabla u|^{p(x)})| \nabla u|^{p(x)-2} \nabla u ...
Hassan Belaouidel +2 more
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Existence and multiplications of solutions for a class of equation with a non-smooth potential [PDF]
Journal of Hyperstructures, 2015 This paper deals with the existence and multiplicity of solutions for a class of nonlocal p−Kirchhoff problem. Using the mountain pass theorem and fountain theorem, we establish the existence of at least one solution and infinitely many solutions for a ...
Fariba Fattahi, M. Alimohammady
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On a nonlinear eigenvalue problem in Sobolev spaces with variable exponent [PDF]
, 2005 We consider a class of nonlinear Dirichlet problems involving the $p(x)$--Laplace operator. Our framework is based on the theory of Sobolev spaces with variable exponent and we establish the existence of a weak solution in such a space.
Dinu, Teodora Liliana
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Schrödinger-Poisson system without growth and the Ambrosetti-Rabinowitz conditions
AIMS Mathematics, 2020 We consider the following Schrödinger-Poisson system $$\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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Extensions of the mountain pass theorem
Journal of Functional Analysis, 1984 The paper contains a number of extensions of the mountain pass lemma of \textit{A. Ambrosetti} and \textit{P. H. Rabinowitz} [(*) ibid. 14, 349-381 (1973; Zbl 0273.49063)]. The lemma gives sufficient conditions for the existence of critical points of continuously Fréchet differentiable functionals \(I: X\to {\mathbb{R}}\) on a real Banach space X.
PUCCI, Patrizia, J. SERRIN
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