The difference equation xn+1=α+xn-k/Σi=0k-1 cixn-i solutions converging to zero

被引：13

作者：

Berenhaut, Kenneth S. ^{[1
]}

Stevic, Stevo

机构：

[1] Wake Forest Univ, Dept Math, Winston Salem, NC 27109 USA

[2] Serbian Acad Sci, Math Inst, Belgrade 11000, Serbia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2007年 / 326卷 / 02期

关键词：

difference equation; positive nonoscillatory solutions; convergence to zero;

D O I：

10.1016/j.jmaa.2006.02.088

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this note is to show that the following difference equation: x(n+1) = alpha + x(n-k)/Sigma(i=0) (k-1)c(i)x(n-i), n=0, 1,..., where k is an element of N, c(i) >= 0, i =0,...,k-1, Sigma(k-1)(i=0)c(i) = 1, and alpha < -1, has solutions which monotonically converge to zero. This result shows the existence of such solutions which was not shown in the recently accepted paper: A.E. Harnza, On the recursive sequence x(n+1) = alpha + x(n-1)/x(n), J. Math. Anal. Appl., in press. (c) 2006 Published by Elsevier Inc.

引用

页码：1466 / 1471

页数：6

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