Topological structure of the solution sets to neutral evolution inclusions driven by measures

Abstract

This study is concerned with topological structure of the solution sets to evolution inclusions of neutral type involving measures on compact intervals. By using Górniewicz-Lassonde fixed-point theorem, the existence of solutions and the compactness of solution sets for neutral measure differential inclusions are obtained. Second, based on the Rδ{R}_{\delta }-structure equivalence theorem, by constructing a continuous function that can make the solution set homotopic at a single point, the Rδ{R}_{\delta }-type structure of the solution sets of this kind of differential inclusion is obtained.

Keywords

• neutral measure evolution inclusions
• existence of solutions
• rδ-set
• measure of noncompactness
• regulated functions
• 28b20
• 34g25
• 35d30