Discontinuous Almost Automorphic Functions and Almost Automorphic Solutions of Differential Equations with Piecewise Constant Argument

2013/06/04 by Alan Chávez, Chavez, A., Samuel Castillo +3 · 1 citation
Mathematics · Medicine · #34D05 #34G10 #47A55 #47D06 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1306.0922

openalex publication_date 2013/06/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this article we introduce a class of discontinuous almost automorphic functions which appears naturally in the study of almost automorphic solutions of differential equations with piecewise constant argument. Their fundamental properties are used to prove the almost automorphicity of bounded solutions of a system of differential equations with piecewise constant argument. Due to the strong discrete character of these equations, the existence of a unique discrete almost automorphic solution of a non-autonomous almost automorphic difference system is obtained, for which conditions of exponential dichotomy and discrete Bi-almost automorphicity are fundamental.

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