On asymptotic behaviour of the difference equation \(x_{n+1} = \alpha+\frac{x_{n-1}^p}{x_n^p}\).
type: Item
instance of: scholarly article
title: On asymptotic behaviour of the difference equation \(x_{n+1} = \alpha+\frac{x_{n-1}^p}{x_n^p}\).
zbMATH Open document ID: 1052.39005
DOI: 10.1007/BF02936179
author: D. Massart
published in: Journal of Applied Mathematics and Computing
publication date: 2004-06-22T00:00:00Z
review text: 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 \(p\geq 1\).
reviewed by: Eduardo Liz
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A20
zbMATH DE Number: 2076571
zbMATH Keywords: difference equations
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: oscillatory solutions
zbMATH Keywords: positive solutions
MaRDI profile type: Publication
cites work: On the recursive sequence \(x_{n+1}=\alpha+x_{n-1}/x_n\)
cites work: Q4458562
cites work: Q3137926
cites work: On rational recursive sequences
cites work: On the recursive sequence \(y_{n+1}=(p+y_{n-1})/(qy_n+y_{n-1})\)
cites work: Q4330105
cites work: Q4519034
full work available at URL: https://doi.org/10.1007/bf02936179
OpenAlex ID: W1974706928
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description: scientific article; zbMATH DE number 2076571