Global behavior of the max-type difference equation \(x_{n+1}=\max\{1/x_{n},A_{n}/x_{n - 1}\}\)
type: Item
instance of: scholarly article
title: Global behavior of the max-type difference equation \(x_{n+1}=\max\{1/x_{n},A_{n}/x_{n - 1}\}\)
zbMATH Open document ID: 1167.39303
DOI: 10.1155/2009/152964
author: Taixiang Sun
author: Bin Qin
author: Hongjian Xi
author: Caihong Han
published in: Abstract and Applied Analysis
publication date: 2009-07-02T00:00:00Z
review text: Summary: We study global behavior of the following max-type difference equation \(x_{n+1}=\max\{1/x_{n},A_{n}/x_{n - 1}\}, n=0,1,\dots,\) where \(\{A_n\}_{n=0}^{\infty}\) is a sequence of positive real numbers with \(0\leq \text{inf} A_{n}\leq \text{sup} A_{n}<1\). The special case when \(\{A_n\}_{n=0}^{\infty}\) is a periodic sequence with period \(k\) and \(A_{n}\in (0,1)\) for every \(n\geq 0\) has been completely investigated by \textit{Y. Chen} [J. Difference Equ. Appl. 11, No.~15, 1289--1294 (2005; Zbl 1086.39003)]. Here, we extend his results to the general case.
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 5574409
Wikidata QID: Q58646534
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2009/152964
OpenAlex ID: W1559031069
cites work: A difference equation with eventually periodic solutions
cites work: Boundedness character of positive solutions of a max difference equation
cites work: Q4938118
cites work: Eventually periodic solutions of \(x_{n+1}=\max\{1/x_ n,A_ n/x_{n-1}\}\).
cites work: Eventual periodicity of with periodic coefficients
cites work: On positive solutions of a reciprocal difference equation with minimum
cites work: On the eventual periodicity of with a period-four parameter
cites work: On \(x_{n+1}=\max \{\frac{1}{x_n},\frac{A_n}{x_{n-1}}\}\) with a period 3 parameter
cites work: Q4650355
cites work: Q4471237
cites work: On the recursive sequence \(x_{n+1}=A+x_{n}^{p}/x_{n-1}^{r}\)
cites work: On the recursive sequence \(x_{n+1} = \max \left\{ c, \frac {x_n^p}{x_{n-1}^p} \right\}\)
cites work: On the asymptotic behavior of a difference equation with maximum
cites work: On the periodicity of the sequence
cites work: Periodic solutions to a difference equation with maximum
cites work: On the periodic nature of the solutions of the reciprocal difference equation with maximum
cites work: Axiomatisations of the average and a further generalisation of monotonic sequences
cites work: On a generalisation of monotonic sequences
cites work: Q4441389
cites work: Q4441394
cites work: Q4441430
cites work: Asymptotic behavior of a sequence defined by iteration with applications
cites work: Asymptotic behavior of a nonlinear difference equation
description: scientific article; zbMATH DE number 5574409