Solutions and multiple solutions for periodic p-Laplacian systems with a non-smooth potential

Abstract

In this article, we study non-linear periodic systems driven by the ordinary vector p-Laplacian differential operator and with a non-smooth potential. Using variational methods based on the non-smooth critical point theory, we prove an existence and a multiplicity theorems. The conditions on the non-smooth potential do not imply that the corresponding Euler functional of the problem is coercive.