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A general method is given in order to guarantee at least one nontrivial solution, as well as infinitely many radially symmetric solutions, for an abstract class of hemivariational inequalities. This abstract class contains some special cases studied by many authors. We remark that, differently from the classical literature, in the proofs we use the Cerami com- pactness condition and the principle of symmetric criticality for locally Lipschitz func- tions. where c> 0 is a positive constant. In what follows, we use only that the functions h1(u) = c|u| and h2(u) = c|u| p−1 are convex, increasing, and h1(0) = h2(0) =0. Let F : R N × R → R be the function defined by

Existence and infinitely many solutions for an abstract class of hemivariational inequalities