Infinitely many solutions to the Neumann problem for elliptic equations involving the p-Laplacian and with discontinuous nonlinearities

In this paper, we establish the existence of infinitely many solutions to a Neumann problem involving the p-laplacian and with discontinuous nonlinearities. The technical approach is mainly basedon a very recent result on critical points for possibly non-smooth functionals in a Banach space due toMarano and Motreanu, namely Theorem 1.1 in a paper that is to appear in the journal J. Diff. Eqns(see Theorem 2.3 in the body of this paper). Some applications are presented.