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  • 1 Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang, 310036, China
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Abstract

We consider the asymptotic stability problems by Lyapunov functionals V for a class of functional differential equations with impulses of the form x′(t)=f(t,xt), xRn, tt0, ttk; △x=Ik(t,x(t)), t=tk, kZ+. Some new asymptotic stability results are presented by using an idea originated by Burton and Makay [6] and developed by Zhang [1]. We generalize some known results about impulsive functional differential equations in the literature in which we only require the derivative of V to be negative definite on a sequence of intervals In=[sn,ξn] which may or may not be contained in the sequence of impulsive time intervals [tn,tn+1).

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Acta Mathematica Hungarica
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