Stability of sets for impulsive functional differential equations via Razumikhin method

被引：0
作者：
Xie S. [1 ]
Shen J. [2 ]
机构：
[1] Department of Mathematics, Hunan Normal University, Changsha
[2] Department of Mathematics, College of Huaihua, Huaihua
来源：
Journal of Mathematical Sciences | 2011年 / 177卷 / 3期
基金：
中国国家自然科学基金;
关键词：
Lyapunov Function; Uniform Stability; Uniform Asymptotic Stability; Impulsive Perturbation; Impulsive Delay;
D O I：
10.1007/s10958-011-0473-9
中图分类号：
学科分类号：
摘要：
In this paper, we consider the functional differential equation with impulsive perturbations {x′(t) = f(t, xt), t≥ t0, t ≠ tk, x ∈ ℝn, Δx(t) = Ik,(t,x(t-)), t = tk, k ∈ ℤ+. Criteria on uniform asymptotic stability of sets are established for the above system using Lyapunov functions and the Razumikhin technique. Some examples are also discussed to illustrate the theorems. © 2011 Springer Science+Business Media, Inc.
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页码：474 / 486
页数：12
相关论文
共 21 条
  • [1] Conway J.B., A Course in Functional Analysis, (1990)
  • [2] Gopalsamy K., Zhang B.G., On delay differntial equations with impulses, J. Math. Anal. Appl., 139, pp. 110-122, (1989)
  • [3] Hale J.K., Theory of Functional Differential Equations, (1977)
  • [4] Kolmanovskii V.B., Nosov V.R., Stability of Functional Differential Equations, (1986)
  • [5] Kulev G.V., Bainov D.D., Stability of sets for impulsive systems, Int. J. Theor. Phys., 28, 2, pp. 195-207, (1989)
  • [6] Kulev G.V., Bainov D.D., Global stability of sets for impulsive differential systems by Lyapunov's direct method, Comput. Math. Appl., 19, 2, pp. 17-28, (1990)
  • [7] Lakshmikantham V., Bainov D.D., Simeonov D.S., Theory of Impulsive Differential Equations, (1989)
  • [8] Lakshmikantham V., Liu X., Stability Analysis in Terms of Two Measures, (1993)
  • [9] Liu X., Ballinger G., Existence and continuability of solutions for differential equations with delay and state-dependent impulses, Nonlin. Anal., 51, pp. 633-647, (2002)
  • [10] Liu X., Ballinger G., Boundedness for impulsive delay differential equations and applications to population growth models, Nonlin. Anal., 53, pp. 1041-1062, (2003)
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