Existence of periodic solution for a class of neutral differential equations with impulses

TL;DR

This paper proves the existence of periodic solutions for impulsive neutral differential equations using Mawhin's continuation theorem, addressing challenges posed by impulse effects through an associated non-impulsive equation.

Contribution

It introduces a novel approach employing a non-impulsive related equation to establish periodic solutions in impulsive neutral differential equations.

Findings

Established sufficient conditions for periodic solutions

Demonstrated solution differentiability between impulses

Addressed impulse effect challenges with a new method

Abstract

By applying a Mawhin's continuation theorem of coincidence degree theory, we establish sufficient conditions for the existence of a periodic solution for a class of impulsive neutral differential equations. The procedure adopted in this work makes use of a non-impulsive associated equation in order to overcome the difficulties resulting from the moments of impulse effects. Under particular assumptions this solution is continuously differentiable on each interval with no impulse effect.