Periodic Solutions for Systems with p-Relativistic Operator and Unbounded Discontinuous Nonlinearities

We are concerned with the existence of periodic solutions for potential differential inclusions involving the p -relativistic operator R p u : = | u ′ | p - 2 u ′ ( 1 - | u ′ | p ) 1 - 1 / p ′ and an (possible) unbounded discontinuous gradient. The approach relies on critical point theory for locally Lipschitz perturbations of convex, lower semicontinuous functions. The solutions we obtain appear as either minimizers or saddle points of the corresponding energy functional. Some examples of applications illustrating the general results are provided.