MULTIPLE SOLUTIONS FOR SEMILINEAR HEMIVARIATIONAL INEQUALITIES AT RESONANCE By LESZEK GASI\’{N}SKI AND NIKOLAOS

Abstract. We consider semilinear eigenvalue problems for hemivariational inequalities at resonance. First we consider problems which are at resonance in a higher eigenvalue $\lambda_{k}$ (with $k\geq 1$ ) and prove two multiplicity theorems asserting the existence of at least $k$ pairs of nontrivial solutions. Then we consider problems which are resonant at the first eigenvalue $\lambda_{1}>0$ . For such problems we prove the existence of at least three nontrivial solutions. Our approach is variational and is based on the nonsmooth critical point theory of Chang, for locally Lipschitz functions.