Multiple nontrivial solutions for nonlinear periodic problems with the p-Laplacian

We consider a nonlinear periodic problem driven by the scalar p-Laplacian with a nonsmooth potential (hemivariational inequality). Using the degree theory for multivalued perturbations of (S)+-operators and the spectrum of a class of weighted eigenvalue problems for the scalar p-Laplacian, we prove the existence of at least three distinct nontrivial solutions, two of which have constant sign.