PROPERTIES OF THE SOLUTION SET OF NONLINEAR EVOLUTION INCLUSIONS

In this paper we examine nonlinear, nonautonomous evolution inclusions defined on a Gelfand triple of spaces. First we show that the problem with a convex-valued, h-usc in x orienter field F(t, x) has a soluti on set which is an R-delta-set in C(T, H). Then for the problem with a nonconvex-valued F(t, x) which is h-Lipschitz in x, we show that the solution set is path-connected in C(T, H). Subsequently we prove a str ong invariance result and a continuity result for the solution multifu nction. Combining these two results we establish the existence of peri odic solutions. Some examples of parabolic partial differential equati ons with multivalued terms are also included.