Topological structure of the solution sets to non-autonomous evolution inclusions driven by measures on the half-line

Abstract

In this article, we investigate a class of measure differential inclusions of evolution type involving non-autonomous operator with nonlocal condition defined on the half-line. By fixed point theorem, we first obtain some sufficient conditions to ensure the solution set is nonempty, compact, and R δ {R}_{\delta } -set on compact interval. Subsequently, by means of the inverse limit method, we generalize the results on compact interval to noncompact interval. Finally, an example is given to demonstrate the effectiveness of obtained results.