Nonlinear evolution inclusions: Topological characterizations of solution sets and applications

This paper deals with a nonlinear delay differential inclusion of evolution type involving m  -dissipative operator and source term of multi-valued type in a Banach space. Under rather mild conditions, the RδRδ-structure of C0C0-solution set is studied on compact intervals, which is then used to obtain the RδRδ-property on non-compact intervals. Secondly, the result about the structure is furthermore employed to show the existence of C0C0-solutions for the inclusion (mentioned above) subject to nonlocal condition defined on right half-line. No nonexpansive condition on nonlocal function is needed. As samples of applications, we consider a partial differential inclusion with time delay and then with nonlocal condition at the end of the paper.