ON MULTIPLE SOLUTIONS FOR STRONGLY RESONANT PROBLEMS WITH THE p-LAPLACIAN

We study a nonlinear elliptic problem driven by the p-Laplacian and with a nonsmooth potential function (hemivariational inequality). On the nonsmooth potential we impose conditions of strong resonance. Following a variational approach based on the nonsmooth critical point theory and the second deformation theorem, we establish the existence of at least two nontrivial smooth solutions.