# Structure of the solution set to Volterra integral inclusions and applications

## TL;DR

This paper investigates the topological structure of solution sets to Volterra integral inclusions in Banach spaces, showing they are nonempty, compact, and acyclic under certain conditions, with applications to periodic problems.

## Contribution

It establishes the topological and geometric properties of solution sets to Volterra integral inclusions, including conditions for acyclicity and applications to periodic problems.

## Key findings

- Solution sets are nonempty and compact
- Solution sets are acyclic or $R_δ$-sets under certain conditions
- Applications to periodic problems are provided

## Abstract

The topological and geometric structure of the solution set to Volterra integral inclusions in Banach spaces is investigated. It is shown that the set of solutions in the sense of Aumann integral is nonempty compact acyclic in the space of continuous functions or is even an $R_\delta$-set provided some appropriate conditions on the Banach space are imposed. Applications to the periodic problem for this type of inclusions are given.