脉冲泛函微分方程的渐近稳定性

罗治国; 罗艳

doi:10.3879/j.issn.1000-0887.2009.10.011

脉冲泛函微分方程的渐近稳定性

doi: 10.3879/j.issn.1000-0887.2009.10.011

罗治国,
罗艳

湖南师范大学数学系,长沙 410081

基金项目: 国家自然科学基金资助项目(10871063);湖南省教育厅(重点)科研基金资助项目(07A038)

详细信息

作者简介:
罗治国(1956- ),男,湖南湘潭人,教授,博士(联系人.Tel:+86-731-88872549;E-mail:luozg@hunnu.edu.cn)

中图分类号: O175
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- 被引次数: 0
出版历程
- 收稿日期: 2009-01-21
- 修回日期: 2009-08-18
- 刊出日期: 2009-10-15

Asymptotic Stability for Impulsive Functional Differential Equations

Department of Mathematics, Hunan Normal University, Changsha 410081, P. R. China

摘要

摘要: 讨论了一类脉冲泛函微分方程的渐近稳定性．通过改进 Liapunov泛函的上界，利用Liapunov泛函第二方法和Jensen不等式，得到了一个一致稳定性定理和一个一致渐近稳定性定理，给出的例子说明了所得结果的优越性
- 稳定性 /
- 脉冲泛函微分方程 /
- Liapunov泛函 /
- Jensen不等式
Abstract: The stability for aclass of mipulsive functional differential equation was inve stigated. By improving the upper bound of Lia punovfunctional and based on the application of the Liapunov second method to gether with Liapunov functional and Jensencs the inequality, auniformly stability theorem and auniformly asymptotically stability theorems are obtained. Examples are also given to demonstrate the a dvantage of our results.
- stability /
- mipulsive functional differential equation /
- Liapunov functional /
- Jensencs inequality

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参考文献(17)

[1]	Lakshmikantham V ， Bainov D D， Simeonov P S.Theory of Impulsive Differential Equations[M]. Singapore:World Scientific，Sin，1989．
[2]	Bainov D D，Simenov P S．Systems With Impulse Effect: Stability Theory and Applications[M].Chichester：Ellis Horwood，1989．
[3]	Samoilenko A M，Perestyuk N A．Impulsive Differential Equations[M].Singapore：World Scientific，1995．
[4]	Shen J，Yan J.Razumikhin type stability theorems for impulsive functional differential equations[J].Nonlinear Anal，1998，33(5):519-531． doi: 10.1016/S0362-546X(97)00565-8
[5]	Liu X ，Shen J.Razumikhin type theorems on boundedness for impulsive functional differential equations[J].Dynamic Systems and Appl，2000，9(3):265-281．
[6]	Zhang Y，Sun J.Stability of impulsive functional differential equations[J].Nonlinear Analysis，2008，68 (12):3665-3678． doi: 10.1016/j.na.2007.04.009
[7]	Luo Z ，Shen J. New Razumikhin type theorems for impulsive functional differential equations[J]. Appl Math Comput，2002，125(2/3):375-386． doi: 10.1016/S0096-3003(00)00139-9
[8]	Liu X ，Ballinger G.Uniformly asymptotic stabilityof impulsive delay differential equations[J]. Computers Math Applic， 2001，41(7/8):903-915． doi: 10.1016/S0898-1221(00)00328-X
[9]	Luo Z， Shen J. Impulsive stabilization of functional differential equations with infinite delays[J]. Appl Math Letters，2003，16(5):695-701． doi: 10.1016/S0893-9659(03)00069-7
[10]	Luo Z，Shen J.Stability of impulsive functional differential equations via Liapunov functional[J].Appl Math Lett， 2009，22(2):163-169． doi: 10.1016/j.aml.2008.03.004
[11]	Shen J，Luo Z，Liu X.Impulsive stabilization of functional differential equations via Liapunov functionals[J]， J Math Anal Appl，1999，240(1/5):1-15．
[12]	Luo Z，Shen J.Stability and boundedness for impulsive functional differential equations with infinite delays[J].Nonlinear Analysis，2001，46(4):475-493． doi: 10.1016/S0362-546X(00)00123-1
[13]	Stamova I M，Stamov G T. Lyapunov-Razumikhin method for impulsive functional differential equations and applications to the population dynamics[J]. J Comput Appl Math，2001，130 (1/2):163-171． doi: 10.1016/S0377-0427(99)00385-4
[14]	Ballinger G，Liu X.Existence and uniqueness results for impulsive delay differential equations[J]. Dynamic Continuous Discrete Impulse Systems，1999，5(1/4):579-591．
[15]	Becker L C ，Burton T A，Zhang S.Functional differential equations and Jensen′s inequality[J]. J Math Anal Appl，1989，138(1):137-156． doi: 10.1016/0022-247X(89)90325-9
[16]	Becker L C ，Burton T A.Jensen′s inequality and Liapunov′s direct method[J]. Cubo A Mathematical J，2004，6(3):65-87．
[17]	Natansoa I P.Theory of Functions of a Real Variable[M].Vol Ⅱ，New York：Ungar，1960．