A multiplicity result for nonlinear second order periodic equations with nonsmooth potential

In this paper we study a quasilinear scalar periodic problem with a non-differentiable potential function. We only assume that, as a function of the state variable, the potential is locally Lipschitz. So the gradient is replaced by the generalized subdifferential in the sense of Clarke. Using a variational approach, based on the nonsmooth critical point theory of Chang (see [1]), we prove the existence of at least three distinct solutions for the periodic problem. An example is also presented, illustrating that our hypotheses on the potential function are realistic.