Abstract
This paper deals with the structural properties of the solution set for a class of nonlinear evolution inclusions with nonlocal conditions. For the nonlocal problems with a convex-valued right-hand side it is proved that the solution set is compact $R_{\delta}$ ; it is the intersection of a decreasing sequence of nonempty compact absolute retracts. Then for the cases of a nonconvex-valued perturbation term it is proved that the solution set is path connected. Finally some examples of nonlinear parabolic problems are given.
Highlights
1 Introduction In this paper, we study the structural properties of the solution set for a class of nonlinear evolution inclusions initiated in [ ] with nonlocal conditions
In the past the topological structure of the solution set of differential inclusions in RN has been investigated by Himmelberg and Van Vleck [ ] and DeBlasi and Myjak [ ]
Himmelberg and Van Vleck considered the topological structure of the solution set to the following differential inclusions: x(t) ∈ F t, x(t), x( ) =, and they showed that the solution set was an Rδ set
Summary
We study the structural properties of the solution set for a class of nonlinear evolution inclusions initiated in [ ] with nonlocal conditions. It has to be noted that the topological structure of the solution set for this type of nonlinear evolution inclusions is an interesting problem which we intend to study in this paper.
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