Structure of the solution set to differential inclusions with impulses at variable times

TL;DR

This paper investigates the topological structure of solution sets for differential inclusions with impulses at variable times, establishing that these sets are $R_{\delta}$-sets, with new results also applicable to differential equations with similar impulses.

Contribution

It introduces an appropriate Banach space framework and proves the solution set forms an $R_{\delta}$-set, extending findings to differential equations with impulses at variable times.

Findings

Solution set is an $R_{\delta}$-set.

Results apply to differential equations with impulses at variable times.

New topological insights into solution structures.

Abstract

A topological structure of the solution set to differential inclusions with impulses at variable times is investigated. In order to do that an appropriate Banach space is defined. It is shown that the solution set is an $R_{\delta}$-set. Results are new also in the case of~differential equations with impulses at variable times.