Abstract and Applied Analysis

Global Behavior of the Difference Equation x n + 1 = ( p + x n - 1 ) / ( q x n + x n - 1 )

Taixiang Sun, Hongjian Xi, Hui Wu, and Caihong Han

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Abstract

We study the following difference equation x n + 1 = ( p + x n - 1 ) / ( q x n + x n - 1 ) , n = 0,1 , , where p , q ( 0 , + ) and the initial conditions x - 1 , x 0 ( 0 , + ) . We show that every positive solution of the above equation either converges to a finite limit or to a two cycle, which confirms that the Conjecture 6.10.4 proposed by Kulenović and Ladas (2002) is true.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 237129, 6 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620730

Digital Object Identifier
doi:10.1155/2010/237129

Mathematical Reviews number (MathSciNet)
MR2660389

Zentralblatt MATH identifier
1203.39007

Citation

Sun, Taixiang; Xi, Hongjian; Wu, Hui; Han, Caihong. Global Behavior of the Difference Equation ${x}_{n+1}=(p+{x}_{n-1})/(q{x}_{n}+{x}_{n-1})$. Abstr. Appl. Anal. 2010 (2010), Article ID 237129, 6 pages. doi:10.1155/2010/237129. https://projecteuclid.org/euclid.aaa/1288620730


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