Opuscula Math. 32, no. 3 (2012), 439-454

Opuscula Mathematica

Existence result for hemivariational inequality involving p(x)-Laplacian

Sylwia Barnaś

Abstract. In this paper we study the nonlinear elliptic problem with \(p(x)\)-Laplacian (hemivariational inequality).We prove the existence of a nontrivial solution. Our approach is based on critical point theory for locally Lipschitz functionals due to Chang [J. Math. Anal. Appl. 80 (1981), 102–129].

Keywords: \(p(x)\)-Laplacian, Palais-Smale condition, mountain pass theorem, variable exponent Sobolev space.

Mathematics Subject Classification: 35A15, 35D30, 35J60, 35M10, 35M87.

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  • Sylwia Barnaś
  • Cracow University of Technology, Institute of Mathematics, ul. Warszawska 24 31-155 Kraków, Poland
  • Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Mathematics, ul. Łojasiewicza 6, 30-348 Kraków, Poland
  • Received: 2011-11-05.
  • Revised: 2012-01-02.
  • Accepted: 2012-01-11.
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Cite this article as:
Sylwia Barnaś, Existence result for hemivariational inequality involving p(x)-Laplacian, Opuscula Math. 32, no. 3 (2012), 439-454, http://dx.doi.org/10.7494/OpMath.2012.32.3.439

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