Properties of the Solution Set of Nonlinear Evolution Inclusions

摘要

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 orientor field F(t,x) has a solution set which is an R_δ-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 strong invariance result and a continuity result for the solution multifunction. Combining these two results we establish the existence of periodic solutions. Some examples of parabolic partial differential equations with multivalued terms are also included.