Almost periodic evolution systems with impulse action at state-dependent moments

TL;DR

This paper investigates the existence of almost periodic solutions in semi-linear parabolic evolution equations with impulses occurring at state-dependent times, providing conditions to prevent the beating phenomenon and illustrating with an impulsive logistic model.

Contribution

It introduces new conditions ensuring almost periodic solutions in impulsive evolution systems with state-dependent impulses, excluding the beating phenomenon.

Findings

Established conditions for almost periodic solutions

Provided criteria to exclude the beating phenomenon

Illustrated results with an impulsive logistic equation example

Abstract

We study the existence of almost periodic solutions for semi-linear abstract parabolic evolution equations with impulse action at state-dependent moments. In particular, we present conditions excluding the beating phenomenon in these systems. The main result is illustrated with an example of impulsive diffusive logistic equation.