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


AKHMET M.

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

  • Publication Type: Article / Article
  • Volume: 16 Issue: 5
  • Publication Date: 2009
  • Journal Name: Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
  • Journal Indexes: Scopus
  • Page Numbers: pp.743-753
  • Keywords: Almost periodic solutions, And phrases. linear systems, Piecewise constant argument, Stability

Abstract

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.