# Degree theory for discontinuous operators

## TL;DR

This paper develops a new topological degree concept for discontinuous operators, enabling fixed point theorems and new existence results for differential equations with discontinuous nonlinearities.

## Contribution

It introduces a novel degree theory for discontinuous operators and applies it to establish existence results for differential equations with discontinuous nonlinearities.

## Key findings

- New topological degree for discontinuous operators
- Fixed point theorems derived for these operators
- Existence results for discontinuous ODEs

## Abstract

We introduce a new definition of topological degree for a meaningful class of operators which need not be continuous. Subsequently, we derive a number of fixed point theorems for such operators. As an application, we deduce a new existence result for first-order ODEs with discontinuous nonlinearities.