Stability of impulsive functional differential equations via the Liapunov functional

被引：51

作者：

Luo, Zhiguo ^{[1
,2
]}

Shen, Jianhua ^{[2
,3
]}

机构：

[1] Jishou Univ, Coll Math & Comp Sci, Jishou 416000, Hunan, Peoples R China

[2] Hunan Normal Univ, Dept Math, Changsha 410081, Hunan, Peoples R China

[3] Coll Huaihua, Dept Math, Huaihua 418008, Hunan, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2009年 / 22卷 / 02期

关键词：

Stability; Impulsive functional differential equation; Liapunov functional; Razumikhin technique; ASYMPTOTIC STABILITY; POPULATION; STABILIZATION; THEOREMS; SYSTEMS; DELAYS;

D O I：

10.1016/j.aml.2008.03.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we investigate the stability of a class of impulsive functional differential equations. Some general stability theorems are obtained. Our results can be applied to finite delay impulsive systems or infinite delay impulsive systems or impulsive systems involving both finite and infinite delays, in a unified way. Examples are also given to illustrate that applying our theorems yields better conclusions than the results in the literature. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：163 / 169

页数：7

共 20 条

[1] Asymptotic stability of competitive systems with delays and impulsive perturbations [J].

Ahmad, Shair ;

Stamova, Ivanka M. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 334 (01) :686-700

[2]

[Anonymous], 1995, World Sci. Ser. Nonlinear Sci., Ser. A., DOI DOI 10.1142/2892

[3]

[Anonymous], 1997, Dynamic Impulse Systems: Theory and Applications

[4]

Bainov D.D., 1989, Systems with Impulse Effect

[5] Analysis of a delayed epidemic model with pulse vaccination and saturation incidence [J].

Gao, Shujing ;

Chen, Lansun ;

Nieto, Juan J. ;

Torres, Angela .

VACCINE, 2006, 24 (35-36) :6037-6045

[6]

Lakshmikantham V., 1989, World scientific, V6

[7] Uniform asymptotic stability of impulsive delay differential equations [J].

Liu, XZ ;

Ballinger, G .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2001, 41 (7-8) :903-915

[8] New Razumikhin type theorems for impulsive functional differential equations [J].

Luo, ZG ;

Shen, JH .

APPLIED MATHEMATICS AND COMPUTATION, 2002, 125 (2-3) :375-386

[9] Impulsive stabilization of functional differential equations with infinite delays [J].

Luo, ZG ;

Shen, JH .

APPLIED MATHEMATICS LETTERS, 2003, 16 (05) :695-701

[10] Stability and boundedness for impulsive functional differential equations with infinite delays [J].

Luo, ZG ;

Shen, JH .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 46 (04) :475-493

← 1 2 →