On the piecewise pseudo almost periodic solution of nondensely impulsive integro-differential systems with infinite delay

TL;DR

This paper establishes the existence of piecewise pseudo almost periodic solutions for a class of neutral impulsive nonlinear integro-differential systems with infinite delay, addressing unresolved problems in the theory.

Contribution

It introduces a novel approach combining integrated semigroup theory and Sadovskii's fixed point theorem to prove solution existence for complex impulsive systems.

Findings

Existence of solutions proven under certain conditions

Application of integrated semigroup theory to impulsive systems

Extension of pseudo almost periodic solution theory to systems with infinite delay

Abstract

In the theory of neutral differential equations with pulse influence (neutral impulsive differential equations), there are many unsolved problems related to certain results in the theory of integral and integro-differential equations. In this article, we present an result for the existence of the piecewise pseudo almost periodic solution of a class of neutral impulsive nonlinear integro-differential systems with infinite delay. The method used involves result on the theory of integrated semigroup as well as the Sadovskii's fixed point theorem.