Opuscula Mathematica
Opuscula Math. 32, no. 3 (), 439-454
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.
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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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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