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.