# Heteroclinic Solutions in Singularly Perturbed Discontinuous Differential Equations

## TL;DR

This paper extends Melnikov theory to discontinuous differential equations, providing conditions for the persistence of heteroclinic solutions under perturbations in such systems.

## Contribution

It introduces Melnikov type conditions specifically for discontinuous differential equations, expanding the applicability of heteroclinic solution analysis.

## Key findings

- Derived Melnikov conditions for discontinuous systems
- Extended continuous system results to discontinuous cases
- Provided criteria for heteroclinic solution persistence

## Abstract

We derive Melnikov type conditions for the persistence of heteroclinic solutions in perturbed slowly varying discontinuous differential equations extending to these equations similar results for continuous differential equations.