Solutions and multiple solutions for periodic systems with nonhomogeneous differential operators

In this paper we consider nonlinear periodic systems driven by the nonhomogeneous vector pp-Laplacian differential operator and with a nonsmooth potential. Using variational techniques, based on the nonsmooth critical point theory, we prove existence and multiplicity results. Finally, we obtain an existence result for systems driven by the ordinary vector pp-Laplacian and we show that it is still true in the more general framework of the previous results.