Nonlinear periodic systems with the p-Laplacian:: Existence and multiplicity results

We study second-order nonlinear periodic systems driven by the vector p-Laplacian with a nonsmooth, locally Lipschitz potential function. Under minimal and natural hypotheses on the potential and using variational methods based on the nonsmooth critical point theory, we prove existence theorems and amultiplicity result. We conclude the paper with an existence theorem for the scalar problem, in which the energy functional is indefinite ( unbounded from both above and below).