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ArticleOriginal scientific text

Title

Existence of a nontrival solution for Dirichlet problem involving p(x)-Laplacian

Authors 1

Affiliations

  1. Cracow University of Technology, Institute of Mathematics, ul. Warszawska 24, 31-155 Kraków, Poland

Abstract

In this paper we study the nonlinear Dirichlet problem involving p(x)-Laplacian (hemivariational inequality) with nonsmooth potential. By using nonsmooth critical point theory for locally Lipschitz functionals due to Chang [6] and the properties of variational Sobolev spaces, we establish conditions which ensure the existence of solution for our problem.

Keywords

ENG
p(x)-Laplacian, hemivariational inequality, Cerami condition, mountain pass theorem, variable exponent Sobolev space

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Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2014/34/1
Export to PBN, Opens in new tab
Pages:
15-39
Main language of publication
English
Received
2013-06-21
Published
2014

DOI: 10.7151/dmdico1154

Exact and natural sciences