On the asymptotic behaviour of Volterra difference equations

被引：3

作者：

Nguyen Van Minh ^{[1
]}

机构：

[1] Columbus State Univ, Dept Math & Philosophy, Columbus, GA 31907 USA

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2013年 / 19卷 / 08期

关键词：

Volterra equation; convolution type; asymptotic almost periodicity; stability; instability; Katznelson-Tzafriri theorem; ALMOST-PERIODIC SOLUTIONS; KATZNELSON-TZAFRIRI TYPE; TAUBERIAN-THEOREMS; INDIVIDUAL ORBITS; DISCRETE; STABILITY;

D O I：

10.1080/10236198.2012.744004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the asymptotic behaviour of solutions of the difference equations of the form x(n + 1) = Ax(n) + Sigma B-n(k=0)(n - k)x(k) + y(n) in a Banach space X, where n=0,1,2,...; A,B(n) are linear bounded operators in X. Our method of study is based on the concept of spectrum of a unilateral sequence. The obtained results on asymptotic stability and almost periodicity are stated in terms of spectral properties of the equation and its solutions. To this end, a relation between the Z-transform and spectrum of a unilateral sequence is established. The main results extend previous results.

引用

页码：1317 / 1330

页数：14

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