Evolution Inclusions with m-Dissipative Operator

Abstract

This chapter deals with a nonlinear delay differential inclusion of evolution type involving m-dissipative operator and source term of multivalued 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 noncompact 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 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 chapter.