具无限时滞的差分方程的一致渐近稳定性

Uniformly Asymptotic Stability for a Class ofDifference Equations with Infinite Delays

本文考虑了如下形式的具无限时滞的差分方程x(n＋1)-x(n)＝F(n,xn),n Z+ ,F:Z＋×Cd(M)→R,这里Cd(M)＝{:Z→R max(m)≤M),获得了零解－致稳定与一致渐近稳定的充分条件．

Consider the following difference equation: x(n + 1 ) - x(n) = F(n,xm),n ∈Z+,where F:Z+ X Cd(M)→ R, Cd(M) = {=Z-→ R ] max (m)≤M}. We obtain sufficientconditions for the uniform stability and uniformly asymptotic stability of the zero solution ofthe above equation.