Multiplicity of solutions for a general \(p(x)\)-Laplacian Dirichlet problem
type: Item
instance of: scholarly article
title: Multiplicity of solutions for a general \(p(x)\)-Laplacian Dirichlet problem
zbMATH Open document ID: 1284.35195
author: F. Kissi
author: A. R. El Amrouss
published in: Arab Journal of Mathematical Sciences
publication date: 2013-10-28T00:00:00Z
full work available at URL: S1319516612000345
review text: This paper deals with a class of nonlinear Dirichlet problems involving the \(p(x)\)-Laplace operator. The main result establishes a sufficient condition for the existence of a weak solution in a related Sobolev space with variable exponent. Next, assuming that the nonlinear term fulfills the Ambrosetti-Rabinowitz condition, the authors establish the existence of at least two distinct solutions. The proofs use standard arguments, including the mountain pass theorem and variational methods.
reviewed by: Teodora-Liliana Rădulescu
Mathematics Subject Classification ID: 35J66
Mathematics Subject Classification ID: 35J92
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 6220519
zbMATH Keywords: \(p(x)\)-Laplace operator
zbMATH Keywords: generalized Lebesgue-Sobolev spaces
zbMATH Keywords: variational method
zbMATH Keywords: multiple solutions
zbMATH Keywords: nonlinear Dirichlet problems
zbMATH Keywords: weak solution
zbMATH Keywords: Sobolev space
zbMATH Keywords: Ambrosetti-Rabinowitz condition
zbMATH Keywords: mountain pass theorem
MaRDI profile type: Publication
OpenAlex ID: W2007234808
cites work: Multiplicity results for quasi-linear problems
cites work: Existence of Solutions for a Class of Problems in IR N Involving the p(x)-Laplacian
cites work: Existence of solutions for \(p(x)\)-Laplacian problems on a bounded domain
cites work: Density of smooth functions in W k, p(x) ( Ω )
cites work: Sobolev embeddings with variable exponent
cites work: OnLp(x)norms
cites work: Existence results to elliptic systems with nonstandard growth conditions
cites work: Solutions for \(p(x)\)-Laplacian Dirichlet problems with singular coefficients
cites work: Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
cites work: Eigenvalues of \(p(x)\)-Laplacian Dirichlet problem
cites work: Q4021390
cites work: Existence and multiplicity of solutions for a Neumann problem involving the \(p(x)\)-Laplace operator
cites work: A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids
cites work: Existence and multiplicity of solutions for a general \(p(x)\)-Laplacian Neumann problem
DOI: 10.1016/J.AJMSC.2012.09.006
description: scientific article; zbMATH DE number 6220519