Extremal solutions and strong relaxation for nonlinear periodic evolution inclusions

We study the existence of extremal periodic solutions for nonlinear evoluti on inclusions defined on an evolution triple of spaces and with the nonline ar operator A being time-dependent and pseudomonotone. Using techniques of multivalued analysis and a surjectivity result for L-generalized pseudomono tone operators, we prove the existence of extremal periodic solutions. Subs equently, by assuming that A(t,.) is monotone, we prove a strong relaxation theorem for the periodic problem. Two examples of nonlinear distributed pa rameter systems illustrate the applicability of our results.