数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (1): 220-236.doi: 10.1016/S0252-9602(17)30128-5

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ASYMPTOTIC EQUIVALENCE OF ALTERNATELY ADVANCED AND DELAYED DIFFERENTIAL SYSTEMS WITH PIECEWISE CONSTANT GENERALIZED ARGUMENTS

Kuo-Shou CHIU   

  1. Departamento de Matemática, Facultad de Ciencias Básicas, Universidad Metropolitana de Ciencias de la Educación, José Pedro Alessandri 774, Santiago, C
  • 收稿日期:2016-12-04 修回日期:2017-01-08 出版日期:2018-02-25 发布日期:2018-02-25
  • 作者简介:Kuo-Shou CHIU,E-mail:kschiu@umce.cl
  • 基金资助:

    This research was in part supported by FGI 05-16 DIUMCE.

ASYMPTOTIC EQUIVALENCE OF ALTERNATELY ADVANCED AND DELAYED DIFFERENTIAL SYSTEMS WITH PIECEWISE CONSTANT GENERALIZED ARGUMENTS

Kuo-Shou CHIU   

  1. Departamento de Matemática, Facultad de Ciencias Básicas, Universidad Metropolitana de Ciencias de la Educación, José Pedro Alessandri 774, Santiago, C
  • Received:2016-12-04 Revised:2017-01-08 Online:2018-02-25 Published:2018-02-25
  • Supported by:

    This research was in part supported by FGI 05-16 DIUMCE.

摘要:

In this paper, we investigate the existence, uniqueness and the asymptotic equivalence of a linear system and a perturbed system of differential equations with piecewise alternately advanced and retarded argument of generalized type (DEPCAG). This is based in the study of an equivalent integral equation with Cauchy and Green matrices type and in a solution of a DEPCAG integral inequality of Gronwall type. Several examples are also given to show the feasibility of results.

关键词: piecewise constant argument of generalized type, hybrid equations, equivalence, asymptotic behavior, Gronwall's inequality

Abstract:

In this paper, we investigate the existence, uniqueness and the asymptotic equivalence of a linear system and a perturbed system of differential equations with piecewise alternately advanced and retarded argument of generalized type (DEPCAG). This is based in the study of an equivalent integral equation with Cauchy and Green matrices type and in a solution of a DEPCAG integral inequality of Gronwall type. Several examples are also given to show the feasibility of results.

Key words: piecewise constant argument of generalized type, hybrid equations, equivalence, asymptotic behavior, Gronwall's inequality