$(\omega,{\rho})$-Periodic solutions of abstract integro-differential impulsive equations on Banach space

TL;DR

This paper studies the existence and uniqueness of special periodic solutions in impulsive integro-differential equations within Banach spaces, expanding understanding of their behavior under impulsive effects.

Contribution

It introduces new conditions ensuring the existence and uniqueness of $( ho, ho)$-periodic solutions for abstract impulsive integro-differential equations on Banach spaces.

Findings

Established sufficient conditions for existence of periodic solutions

Proved uniqueness of these solutions under certain assumptions

Extended previous results to a broader class of equations

Abstract

In this paper, we investigate the existence and uniqueness of $(\omega,{\rho})$-periodic solutions for a class of the abstract impulsive integro-differential equations on Banach space.