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

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  • Taixiang Sun
  • Hongjian Xi
  • Hui Wu

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.

Suggested Citation

  • Taixiang Sun & Hongjian Xi & Hui Wu, 2006. "On boundedness of the solutions of the difference equation x n + 1 = x n − 1 / ( p + x n )," Discrete Dynamics in Nature and Society, Hindawi, vol. 2006, pages 1-7, September.
    • Handle: RePEc:hin:jnddns:020652
    DOI: 10.1155/DDNS/2006/20652
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    Cited by:

    1. Stević, Stevo, 2009. "Boundedness character of a fourth order nonlinear difference equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2364-2369.

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