Exponentially dichotomous linear systems of differential equations with piecewise constant argument

AKHMET M.

Discontinuity, Nonlinearity, and Complexity, vol.1, no.4, pp.337-352, 2012 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 1 Issue: 4
  • Publication Date: 2012
  • Doi Number: 10.5890/dnc.2012.09.001
  • Journal Name: Discontinuity, Nonlinearity, and Complexity
  • Journal Indexes: Scopus
  • Page Numbers: pp.337-352
  • Keywords: Almost periodic solutions, Exponential dichotomy, Periodic solutions, Piecewise constant argument
  • Middle East Technical University Affiliated: Yes

Abstract

© 2012 L & H Scientific Publishing, LLC.We consider differential equations with piecewise constant argument of generalized type. It is the first time, an attention is given to the exponential dichotomy of linear systems. Bounded, almost periodic and periodic solutions and their stability are discussed. The study is made in such a way that further construction of the theory will follow for ordinary differential equations. The results are illustrated by examples.