Almost periodic solutions of the linear differential equation with piecewise constant argument


Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, vol.16, no.5, pp.743-753, 2009 (Scopus) identifier


The paper is concerned with the existence and stability of almost periodic solutions of linear systems with piecewise constant argument where t∈R, x ∈ Rn [·] is the greatest integer function. The Wexler inequality [1]-[4] for the Cauchy's matrix is used. The results can be easily extended for the quasilinear case. A new technique of investigation of equations with piecewise argument, based on an integral representation formula, is proposed. Copyright © 2009 Watam Press.