Existence and multiplicity results for some elliptic systems with discontinuous nonlinearities

In this paper we complete two tasks. We first extend the critical point theorem obtained by Li and Willem S.J. Li, M. Willem, Applications of local linking to critical point theory, J. Math. Anal. Appl. 189 (1995), 6-32] to the nonsmooth case in which the energy functional is locally Lipschitz and satisfies the weaker nonsmooth Cerami condition. Then we study some semilinear elliptic systems with discontinuous nonlinearities and obtain some existence and multiplicity results.