Opuscula Math. 32, no. 3 (2012), 439-454
http://dx.doi.org/10.7494/OpMath.2012.32.3.439
Opuscula Mathematica
Existence result for hemivariational inequality involving p(x)-Laplacian
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.
- 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.
