Nonautonomous second order periodic systems: existence and multiplicity of solutions

In this paper we study the existence and multiplicity of solutions for a second order nonautonumous periodic system with a nonsmooth potential. We prove two existence theorems and a multiplicity result. In the first existence theorem the Euler functional is coercive and the solution is a minimizer of it. In the second existence theorem the Euler functional is unbounded and the solution is obtained using the saddle point theorem. Finally for the multiplicity result we employ a nonsmooth version of the local linking theorem.