Solutions and multiple solutions for second order periodic systems with a nonsmooth potential

A nonautonomous second order system with a nonsmooth potential is studied. Using the nonsmooth critical point theory, first an existence theorem is proved. Then, bystrengthening the hypotheses on the nonsmooth potential, amultiplicity theorem is proved using the nonsmooth second deformation. The hypotheses on the nonsmooth potential make the Euler functional of the problem bounded below but do not make it coercive. Moreover, the analytical framework of the paper incorporates strongly resonant periodic systems.