Almost periodic solutions of differential equations with piecewise constant argument of generalized type

2006/02/14 by Marat Akhmet, Akhmet, M. U.
Mathematics · #34K14 #34K20 #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.math/0602309

openalex publication_date 2006/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider existence and stability of an almost periodic solution of the quasilinear system of differential equations with piecewise constant argument of generalized type. The associated linear homogeneous system satisfies exponential dichotomy. The deviations of the argument are not restricted by any sign assumption when existence is considered. The problem of positive (almost periodic) solutions of the logistic equation is discussed as an example. A new technique of investigation of equations with piecewise argument, based on integral representation, is developed.

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