Multiple solutions for nonlinear periodic systems with combined nonlinearities and a nonsmooth potential

We consider nonlinear periodic systems driven by the p-Laplacian and with a nonsmooth locally Lipschitz potential function. In the right hand side forcing term, we have the combined effects of p-sublinear (concave) and p-superlinear (convex) terms. However, the p-superlinear term need not satisfy the Ambrosetti-Rabinowitz condition. By combining nonsmooth critical point theory with the Ekeland variational principle, we show that the system has at least two nontrivial periodic solutions.