The periodicity of positive solutions of the nonlinear difference equation \(x_{n+1} = \alpha + (x^p_{n-k})/(x^q_n)\)
type: Item
instance of: scholarly article
title: The periodicity of positive solutions of the nonlinear difference equation \(x_{n+1} = \alpha + (x^p_{n-k})/(x^q_n)\)
zbMATH Open document ID: 1264.39014
DOI: 10.1155/2013/742912
author: Mehmet Gümüş
published in: Discrete Dynamics in Nature and Society
publication date: 2013-06-13T00:00:00Z
review text: Summary: We give a remark about the periodic character of positive solutions of the difference equation \(x_{n+1} = \alpha + x^p_{n-k}/x^q_n\), \(n = 0, 1, \dots\), where \(k > 1\) is an odd integer, \(\alpha, p, q \in (0, \infty)\) and the initial conditions \(x_{-k}, \dots, x_0\) are arbitrary positive numbers.
Mathematics Subject Classification ID: 39A23
zbMATH DE Number: 6175116
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/742912
OpenAlex ID: W1966585143
Wikidata QID: Q58921793
cites work: On the recursive sequence \(x_{n+1}=A+(x_{n - 1}^p/x_n^q)\)
cites work: On the dynamics of the recursive sequence \(x_{n+1} = \alpha + x^p_{n-k}/x^q_n\)
cites work: On the recursive sequence \(x_{n+1}=\alpha+x_{n-1}/x_n\)
cites work: The dynamics of the solutions of some difference equations
cites work: Solution and attractivity for a rational recursive sequence
description: scientific article; zbMATH DE number 6175116