Global Behavior of the Difference Equation xn+1 = (p + xn−1)/(qxn + xn−1)

Taixiang Sun, Hongjian Xi, Hui Wu and Caihong Han

Abstract and Applied Analysis, 2010, vol. 2010, issue 1

Abstract: We study the following difference equation xn+1 = (p + xn−1)/(qxn + xn−1), n = 0,1, …, where p, q ∈ (0, +∞) and the initial conditions x−1, x0 ∈ (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.

Date: 2010
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https://doi.org/10.1155/2010/237129

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:237129

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