On quasi-periodic solutions of differential equations with piecewise constant argument

被引：29

作者：

Küpper, T

Yuan, R

机构：

[1] Univ Cologne, Inst Math, D-50931 Cologne, Germany

[2] Beijing Normal Univ, Dept Math, Beijing 100875, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2002年 / 267卷 / 01期

基金：

中国国家自然科学基金;

关键词：

quasi-periodic solutions; quasi-periodic sequences; piecewise constant argument;

D O I：

10.1006/jmaa.2001.7761

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the existence of quasi-periodic solutions to differential equations with piecewise constant argument (EPCA, for short). It is shown that EPCA with periodic perturbations possess a quasi-periodic solution and no periodic solution. The appearance of quasi-periodic rather than periodic solutions is due to the piecewise constant argument. This new phenomenon illustrates a crucial difference between ODE and EPCA. The results are extended to nonlinear equations. (C) 2002 Elsevier Science (USA).

引用

页码：173 / 193

页数：21

共 50 条

[1] Almost periodic solutions of linear differential equations with piecewise constant argument
Yuan, R
Hong, JL
CHINESE ANNALS OF MATHEMATICS SERIES B, 1998, 19 (01) : 59 - 64
[2] Existence of almost periodic solutions of neutral differential equations with piecewise constant argument
袁荣
洪佳林
Science China Mathematics, 1996, (11) : 1164 - 1177
[3] Existence of almost periodic solutions of neutral differential equations with piecewise constant argument
Yuan, R
Hong, JL
SCIENCE IN CHINA SERIES A-MATHEMATICS, 1996, 39 (11): : 1164 - 1177
[4] Remotely almost periodic solutions to systems of differential equations with piecewise constant argument
Zhang, Chuanyi
Jiang, Lina
APPLIED MATHEMATICS LETTERS, 2008, 21 (08) : 761 - 768
[5] Almost periodic type solutions of some differential equations with piecewise constant argument
Hong, JL
Obaya, R
Sanz, A
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 45 (06) : 661 - 688
[6] The existence of almost periodic solutions for a class of differential equations with piecewise constant argument
Rong, Y
Hong, JL
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 28 (08) : 1439 - 1450
[7] The existence of almost periodic solutions of retarded differential equations with piecewise constant argument
Yuan, R
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 48 (07) : 1013 - 1032
[8] Almost periodic solutions of a class of singularly perturbed differential equations with piecewise constant argument
Yuan, R
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1999, 37 (07) : 841 - 859
[9] ALMOST AUTOMORPHIC SOLUTIONS FOR DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT
Zhang, Li-Li
Li, Hong-Xu
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2014, 90 (01) : 99 - 112
[10] Almost periodic weak solutions of neutral delay-differential equations with piecewise constant argument
Li, HX
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (03) : 530 - 545

← 1 2 3 4 5 →