LUO Zhi-guo, LUO Yan. Asymptotic Stability for Impulsive Functional Differential Equations[J]. Applied Mathematics and Mechanics, 2009, 30(10): 1234-1242. doi: 10.3879/j.issn.1000-0887.2009.10.011
Citation: LUO Zhi-guo, LUO Yan. Asymptotic Stability for Impulsive Functional Differential Equations[J]. Applied Mathematics and Mechanics, 2009, 30(10): 1234-1242. doi: 10.3879/j.issn.1000-0887.2009.10.011

Asymptotic Stability for Impulsive Functional Differential Equations

doi: 10.3879/j.issn.1000-0887.2009.10.011
  • Received Date: 2009-01-21
  • Rev Recd Date: 2009-08-18
  • Publish Date: 2009-10-15
  • 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.
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  • [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.
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