Existence results for a Neumann problem involving the p(x)-Laplacian with discontinuous nonlinearities

In this paper the existence of a nontrivial solution to a parametric Neumann problem for a class of nonlinear elliptic equations involving the p(x)-Laplacian and a discontinuous nonlinear term is established. Under a suitable condition on the behavior of the potential at 0(+), we obtain an interval ]0, lambda*], such that, for any lambda is an element of ]0, lambda*] our problem admits at least one nontrivial weak solution. The solution is obtained as a critical point of a locally Lipschitz functional. In addition to providing a new conclusion on the existence of a solution even for lambda = lambda*, our theorem also includes other results in the literature for regular problems. (C) 2015 Elsevier Ltd. All rights reserved.