Nontrival solution for nonlinear p(x)-Laplacian Dirichlet problem with the sign-changing weight

Abstract

In this paper we study the nonlinear elliptic problem involving p(x)-Laplacian with nonsmooth potential, where the weighted function may change sign. By using critical point theory for locally Lipschitz functionals due to Chang, we obtain conditions which ensure the existence of a solution for our problem.

17 pages. arXiv admin note: substantial text overlap with arXiv:1212.4482, arXiv:1212.3688