扰动的中立型时滞差分方程的一致渐近稳定性

陈武华;关治洪;卢小梅

数学学报 ›› 2005, Vol. 48 ›› Issue (1) : 63-74.

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PDF(455 KB)
数学学报 ›› 2005, Vol. 48 ›› Issue (1) : 63-74. DOI: 10.12386/A2005sxxb0007
论文

扰动的中立型时滞差分方程的一致渐近稳定性

    陈武华;关治洪;卢小梅
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Uniform Asymptotic Stability for Perturbed Neutral Delay Difference Equations

    Wu Hua CHEN(1), Zhi Hong GUAN(
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摘要

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.

Abstract

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.

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中立型差分方程 / 时滞 / 一致渐近稳定性

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陈武华;关治洪;卢小梅. 扰动的中立型时滞差分方程的一致渐近稳定性. 数学学报, 2005, 48(1): 63-74 https://doi.org/10.12386/A2005sxxb0007
Wu Hua CHEN(1), Zhi Hong GUAN(. Uniform Asymptotic Stability for Perturbed Neutral Delay Difference Equations. Acta Mathematica Sinica, Chinese Series, 2005, 48(1): 63-74 https://doi.org/10.12386/A2005sxxb0007
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