Electronic Journal of Differential Equations, Vol. 2004(2004), No. 37, pp. 1-17. Title: An existence result for hemivariational inequalities Authors: Zsuzsanna Dalyay (Univ. of Szeged, Hungary) Csaba Varga ("Babes-Bolyai" Univ., Romania) Abstract: We present a general method for obtaining solutions for an abstract class of hemivariational inequalities. This result extends many results to the nonsmooth case. Our proof is based on a nonsmooth version of the Mountain Pass Theorem with Palais-Smale or with Cerami compactness condition. We also use the Principle of Symmetric Criticality for locally Lipschitz functions. Submitted November 17, 2003. Published March 16, 2004. Math Subject Classifications: 35A15, 35J60, 35H30. Key Words: Variational methods; discontinuous nonlinearities; principle of symmetric criticality.