On the Recursive Sequence x n + 1 = A + x n p / x n − 1 r

Stevo Stevic

Discrete Dynamics in Nature and Society, 2007, vol. 2007, 1-9

Abstract:

The paper considers the boundedness character of positive solutions of the difference equation x n + 1 = A + x n p / x n − 1 r , n ∈ ℕ 0 , where A , p , and r are positive real numbers. It is shown that (a) If p 2 ≥ 4 r > 4 , or p ≥ 1 + r , r ≤ 1 , then this equation has positive unbounded solutions; (b) if p 2 < 4 r , or 2 r ≤ p < 1 + r , r ∈ ( 0 , 1 ) , then all positive solutions of the equation are bounded. Also, an analogous result is proved regarding positive solutions of the max type difference equation x n + 1 = max { A , x n p / x n − 1 r } , where A , p , q ∈ ( 0 , ∞ ) .

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:040963

DOI: 10.1155/2007/40963

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