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.
Applied Mathematics and Optimization – Springer Journals
Published: Jul 1, 1997
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