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