文章基本信息
- 标题：On the Solutions of Systems of Difference Equations
- 本地全文：下载
- 作者：İbrahim Yalçinkaya ; Cengiz Çinar ; Muhammet Atalay 等
- 期刊名称：Advances in Difference Equations
- 印刷版ISSN：1687-1839
- 电子版ISSN：1687-1847
- 出版年度：2008
- 卷号：2008
- DOI：10.1155/2008/143943
- 出版社：Hindawi Publishing Corporation
- 摘要：
We show that every solution of the following system of difference equations x n + 1 ( 1 ) = x n ( 2 ) / ( x n ( 2 ) − 1 ) , x n + 1 ( 2 ) = x n ( 3 ) / ( x n ( 3 ) − 1 ) , … , x n + 1 ( k ) = x n ( 1 ) / ( x n ( 1 ) − 1 ) as well as of the system x n + 1 ( 1 ) = x n ( k ) / ( x n ( k ) − 1 ) , x n + 1 ( 2 ) = x n ( 1 ) / ( x n ( 1 ) − 1 ) , … , x n + 1 ( k ) = x n ( k − 1 ) / ( x n ( k − 1 ) − 1 ) is periodic with period 2 k if k ≠ 0 ( mod 2), and with period k if k = 0 ( mod 2) where the initial values are nonzero real numbers for x 0 ( 1 ) , x 0 ( 2 ) , … , x 0 ( k ) ≠ 1 .
