Periodic Problems for Strongly Nonlinear Second-Order Differential Inclusions

In this paper, we study periodic problems for second-order differential inclusions in N with a maximal monotone term. The nonlinear differential operator is not necessarily homogeneous, does not obey any growth condition and incorporates as a special case the one-dimensional p-Laplacian. Using techniques from multivalued analysis and the theory of operators of monotone type, we prove the existence of solutions for both the “convex” and “nonconvex” problems, when the maximal monotone term A is defined everywhere and when it is not defined everywhere (case of variational inequalities).