Existence of a nontrival solution for Dirichlet problem involving   p(x)-Laplacian
  In this paper we study the nonlinear Dirichlet problem involving p(x)-Laplacian (hemivariational inequality) with nonsmooth potential. By using nonsmooth critical point theory for locally Lipschitz functionals due to Chang and the properties of variational Sobolev spaces, we establish conditions which ensure the existence of solution for our problem. 
Sylwia Barna\'s
math.AP