Abstract :
In this paper, sufficient conditions are given for asymptotic stability and uniformly asymptotic stability
of impulsive functional differential equation of the form
x (t) = f (t,xt ), t t0,
x = Ik(t, x(t−)), t = tk, k ∈ Z+,
and the conditions in theorems extend or improve the corresponding ones in [J. Yan, J. Shen, Impulsive
stabilization of functional differential equation by Liapunov–Razumikhin functions, Nonlinear Anal. 37
(1999) 245–255; J. Shen, Z. Luo, Impulsive stabilization of functional differential equations via Liapunov
functionals, J. Math. Anal. Appl. 240 (1999) 1–15; L. Hatvani, On the asymptotic stability for nonautonomous
functional differential equations by Liapunov functionals, Trans. Amer. Math. Soc. 354 (2002)
3555–3571].
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