Properties of the solution set of nonlinear evolution inclusions

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 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

Properties of the solution set of nonlinear evolution inclusions

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Copyright © 1997 by Springer-Verlag New York Inc.
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
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