扰动的中立型时滞差分方程的一致渐近稳定性

本文研究扰动的一维中立型时滞差分方程△(x(n)-cx(n-k))=f(n,xn)+g(n,xn),n∈Z+的稳定性问题.证明了在某些条件下,无扰动方程△(x(n)-cx(n-k))=f(n,xn),n∈Z+零解的一致渐近稳定性蕴涵着上述扰动方程零解的一致渐近稳定性.本文的结果推广并改进了已有的结果.

Uniform Asymptotic Stability for Perturbed Neutral Delay Difference Equations

In this paper, a one-dimensional perturbed neutral delay difference equation of the form: △(x(n) - cx(n - k)) = f(n,xn) + g(n,xn), n ∈ Z+ is considered. It is shown that under some conditions, the zero solution of the above equation is uniformly asymptotically stable provided that the zero solution of the corresponding equationwithout perturbation: △(x(n) - cx(n - k)) = f(n,xn), n∈Z+ is uniformly asymptotically stable. Some known results associated with this equation are extended and improved.