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On asymptotic behaviour of the difference equation \(x_{n+1} = \alpha+\frac{x_{n-1}^p}{x_n^p}\). (English) Zbl 1052.39005

The authors investigate the oscillation with respect to the equilibrium, and the asymptotic behaviour of the positive solutions to the difference equation \[ x_{n+1}=\alpha+(x_{n-1}/x_n)^p,\, n=0,1,\dots, \] where \(\alpha\geq 0\) and \(p\geq 1\).
Reviewer: Eduardo Liz (Vigo)

MSC:

39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations
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References:

[1] Amleh, A. M.; Grove, E. A.; Georgion, D. A.; Ladas, G., On the recursive sequence \(x_{n + 1} = \alpha + \frac{{x_{n - 1} }}{{x_n }} \), J. Math. Anal. Appl., 233, 790-798 (1999) · Zbl 0962.39004 · doi:10.1006/jmaa.1999.6346
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