# Nonlinear Evolution Inclusions: Topological Characterizations of Solution Sets and Applications

Rong-Nian Wang^{*}

In this talk we focus on 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 $R_\delta$-structure of $C^0$-solution set is studied on compact intervals, which is then used to obtain the $R_\delta$-property on non-compact intervals. Secondly, the result about the structure is furthermore employed to show the existence of $C^0$-solutions for the inclusion (mentioned above) subject to a 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.

Mathematics Subject Classification: 35A30 34K09

Keywords: Nonlinear delay evolution inclusion; $R_\delta$-structure; Inverse limit; Nonlocal condition; Frechet space

Minisymposion: Analysis and Control of Evolution Equations and Inclusions