A new view of the lp-theory for a system of higher order difference equations

被引：8

作者：

Gyori, I. ^{[1
]}

Horvath, L. ^{[1
]}

机构：

[1] Univ Pannonia, Dept Math, H-8200 Veszprem, Hungary

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2010年 / 59卷 / 08期

关键词：

Difference equations; l(p) solutions; Companion matrix;

D O I：

10.1016/j.camwa.2010.02.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is proved under appropriate assumptions that the solutions of a linear system of higher order difference equations belong to l(p), that is the pth powers of the solutions are summable for some p >= 1. Our results are based on a new transformation of the higher order system into a first-step recursion, where the companion matrices are well treatable from our point of view. Our theory is illustrated by examples, including an interesting exponential stability result and a class of linear delay difference equations. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：2918 / 2932

页数：15

共 7 条

[1] [Anonymous], FUNCTIONAL DIFFERENT
[2] Exponential Stability of Difference Equations with Several Delays: Recursive Approach
Berezansky, Leonid
Braverman, Elena
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2009,
[3] Elaydi S. N., 1996, An Introduction to Difference Equations
[4] Asymptotic behavior of recursions via fixed point theory
Ey, Kristine
Poetzsche, Christian
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 337 (02) : 1125 - 1141
[5] Nonlinear volterra difference equations in space lp
Gil', MI
Medina, R
[J]. DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2004, 2004 (02) : 301 - 306
[6] Gordon S. P., 1971, Mathematical Systems Theory, V5, P56, DOI 10.1007/BF01691467
[7] Existence of complex l2 solutions of linear delay systems of difference equations
Petropoulou, EN
Siafarikas, PD
[J]. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2005, 11 (01) : 49 - 62

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