Existence and Stability of Almost Periodic Solutions of Differential Equations with Generalized Piecewise Constant Argument

TL;DR

This paper investigates the existence and stability of almost periodic solutions in differential equations with generalized piecewise constant arguments and almost periodic coefficients, extending linear equations with exponential dichotomy.

Contribution

It establishes conditions for the existence and stability of almost periodic solutions in a new class of differential equations with generalized piecewise constant arguments.

Findings

Existence of almost periodic solutions under specified conditions

Stability of solutions on a semi-axis

Extension of exponential dichotomy concepts to these equations

Abstract

This work deals with the existence of an almost periodic solution for certain kind of differential equations with generalized piecewise constant argument, almost periodic coefficients which are seen as a perturbation of a linear equation of that kind satisfying an exponential dichotomy on a difference equation. The stability of that solution in a semi-axis studied.