# Guiding potential method for differential inclusions with nonlocal conditions

## TL;DR

This paper introduces a guiding potential method combined with topological degree theory to establish the existence of solutions for nonlocal initial value problems involving differential inclusions, and discusses the compactness of their solution sets.

## Contribution

It presents a novel approach using the guiding potential method and topological degree theory to solve nonlocal differential inclusions, extending existing solution existence results.

## Key findings

- Existence of solutions for certain nonlocal differential inclusions is proven.
- Conditions for compactness of the solution set are established.
- The guiding potential method is effectively applied to multivalued vector fields.

## Abstract

The existence of solutions of some nonlocal initial value problems for differential inclusions is established. The guiding potential method is used and the topological degree theory for admissible multivalued vector fields is applied. Some conclusions concerning compactness of the solution set have been drawn.