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http://dx.doi.org/10.1016/j.jat.2008.01.007

has been cited by the following article:

• TITLE: New Asymptotical Stability and Uniformly Asymptotical Stability Theorems for Nonautonomous Difference Equations

  AUTHORS: Limin Zhang, Chaofeng Zhang

  KEYWORDS: Nonautonomous Difference Equations, New Asymptotical Stability Theorem, New Uniformly Asymptotical Stability Theorem, Liapunovs Direct Method

  JOURNAL NAME: Applied Mathematics, Vol.7 No.10, June 7, 2016

  ABSTRACT: New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous difference equations relies on the existence of a positive definite Liapunov function that has an indefinitely small upper bound and whose variation along a given nonautonomous difference equations is negative definite. In this paper, we consider the case that the Liapunov function is only positive definite and its variation is semi-negative definite. At these weaker conditions, we put forward a new asymptotical stability theorem of nonautonomous difference equations by adding to extra conditions on the variation. After that, in addition to the hypotheses of our new asymptotical stability theorem, we obtain a new uniformly asymptotical stability theorem of nonautonomous difference equations provided that the Liapunov function has an indefinitely small upper bound. Example is given to verify our results in the last.