On boundedness of the solutions of the difference equation x n + 1 = x n − 1 / ( p + x n )

Taixiang Sun, Hongjian Xi and Hui Wu

Discrete Dynamics in Nature and Society, 2006, vol. 2006, 1-7

Abstract:

We study the difference equation x n + 1 = x n − 1 / ( p + x n ) , n = 0 , 1 , … , where initial values x − 1 , x 0 ∈ ( 0 , + ∞ ) and 0 < p < 1 , and obtain the set of all initial values ( x − 1 , x 0 ) ∈ ( 0 , + ∞ ) × ( 0 , + ∞ ) such that the positive solution { x n } n = − 1 ∞ is bounded. This answers the Open Problem 2 proposed by Kulenović and Ladas.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:020652

DOI: 10.1155/DDNS/2006/20652

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