On boundedness of the solutions of the difference equation \(x_{n+1}=x_{n-1}/(p+x_{n})\)
type: Item
instance of: scholarly article
title: On boundedness of the solutions of the difference equation \(x_{n+1}=x_{n-1}/(p+x_{n})\)
zbMATH Open document ID: 1149.39301
DOI: 10.1155/DDNS/2006/20652
author: Taixiang Sun
author: Hongjian Xi
author: Hui Wu
published in: Discrete Dynamics in Nature and Society
publication date: 2008-07-28T00:00:00Z
review text: Summary: We study the difference equation \(x_{n+1}=x_{n-1}/(p+x_n)\), \(n=0,1,\dots\), where initial values \(x_{-1},x_0\in(0,+\infty)\) and \(0<p<1\), and obtain the set of all initial values \((x_{-1},X_0)\in (0,+\infty)\times (0,+\infty)\) such that the positive solution \(\{x_n\}_{n=-1}^\infty\) is bounded. This answers the open problem 2 proposed by \textit{M. R. S. Kulenović} and \textit{G. Ladas} [Dynamics of second order rational difference equations. With open problems and conjectures. Boca Raton, FL: Chapman \& Hall/CRC (2002; Zbl 0981.39011)].
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A20
zbMATH DE Number: 5304368
zbMATH Keywords: rational difference equation
zbMATH Keywords: bounded solutions
zbMATH Keywords: global asymptotic stability
MaRDI profile type: Publication
cites work: Q4458562
cites work: Dynamics of second order rational difference equations. With open problems and conjectures
full work available at URL: https://doi.org/10.1155/ddns/2006/20652
OpenAlex ID: W1495247067
description: scientific article; zbMATH DE number 5304368