# On nonlocal Cauchy problems for constrained differential inclusions in Euclidean space

## TL;DR

This paper establishes existence results for constrained nonlinear differential inclusions with nonlocal boundary conditions in Euclidean space, using viability theorems and the bound set technique with non-differentiable bounds.

## Contribution

It introduces new viability theorems for differential inclusions with geometric regularity and applies the bound set technique to Floquet boundary problems.

## Key findings

- Existence of solutions under geometric regularity conditions
- Application of bound set technique with non-differentiable bounds
- Development of viability theorems for constrained differential inclusions

## Abstract

We investigate the existence of solutions of constrained nonlinear differential inclusions with nonlocal boundary conditions. Our viability theorems are based on the assumption that the right-hand side of differential inclusion is defined on the domain possessing a certain type of geometric regularity, expressed in terms of locally Lipschitz functional constraints. For solvability of the Floquet boundary value problems associated with differential inclusions we engage the bound set technique. It relies on the usage of not necessarily differentiable bounding functions.