Volterra nonautonomous evolution inclusions: topological structure of solution sets and applications

Abstract

This paper concerns with a class of Volterra nonautonomous evolution inclusions with time delay effect defined on a noncompact interval. It involves a family of (possibly unbounded) operators, which generates a noncompact evolution family. In the framework of Fréchet spaces, the topological structure of the solution set for evolution inclusion is considered. Moreover, we obtain geometric features of the corresponding solution map. Our results extend essentially the existing ones which do not involve Volterra integral in nonlinearity. We finally present a concrete example to illustrate the abstract results.