Existence of periodic solutions of nonlinear evolution inclusions in Banach spaces

In this paper, we consider nonlinear evolution problems, defined on an evolution triple of spaces, driven by a monotone operator, and with a perturbation term which is multivalued. We prove existence theorems of periodic solutions for the cases of a convex and of a nonconvex valued perturbation term which is defined on all of I × H with values in V^* (here V ⊂ H ⊂ V^* is the evolution triple). Also, we prove the existence of extremal periodic solutions and a strong relaxation theorem. Some examples of nonlinear parabolic problems are presented.