On the asymptotic stability of linear Volterra difference equations of convolution type

被引：11

作者：

Elaydi, S. ^{[1
]}

Messina, E.

Vecchio, A.

机构：

[1] Trinity Univ, Dept Math, San Antonio, TX 78212 USA

[2] Univ Studi Napoli Federico 2, Dipartimento Matemat & Applicaz, I-80126 Naples, Italy

[3] CNR, Ist Appl Calcolo M Picone Sede Napoli, I-80131 Naples, Italy

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2007年 / 13卷 / 12期

关键词：

Volterra difference equations; asymptotic stability; convolution; open question;

D O I：

10.1080/10236190701264529

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the condition vertical bar a vertical bar + vertical bar Sigma(+)(l=0)vertical bar < 1 is not necessary, though sufficient, for the asymptotic stability of x(n+1) ax(n) +Sigma(+)(l)(=0) b(n-1x1). We prove the existence of a class of Volterra difference equations (VDEs) that violate this condition but whose zero solutions are asymptotically stable.

引用

页码：1079 / 1084

页数：6

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