Variational methods for nonlinear, nonsmooth second-order periodic systems

摘要

In this article, we examine nonlinear, nonautonomous second-order systems driven by the vector ordinary p-Laplacian and with a nonsmooth potential. In the first half of the article, we investigate systems with an energy (Euler) functional which is indefinite and in general noncompact and nonconvex. Using a nonsmooth version of the saddle point reduction technique, we prove two existence theorems. In the second half of the article, we study problems with a bounded below (definite) energy functional. We prove two multiplicity results and an existence theorem for a strongly resonant at the zero eigenvalue system. Our methods are variational and use notions and techniques from nonsmooth critical point theory.