On the periodic nature of the solutions of the reciprocal difference equation with maximum
type: Item
instance of: scholarly article
title: On the periodic nature of the solutions of the reciprocal difference equation with maximum
zbMATH Open document ID: 1053.39023
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-20T00:00:00Z
review text: The author investigates the periodic nature of the positive solutions of the difference equation \[ x_n=\max\bigg\{\frac{A}{x_{n-1}},\frac{B}{x_{n-2}},\frac{C}{x_{n-3}}\bigg\}, \;n=0,1,\dots,\eqno{(E)} \] where \(A,B,C\) are any positive coefficients, and the initial values \(x_{-1},x_{-2},x_{-3}\) are any positive numbers. The author proves that every positive solution of the equation (\(E\)) is eventually periodic of (not necessarily prime) period \(T\), which is explicitly determined by the coefficients \(A,B\) and \(C\).
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A20
zbMATH DE Number: 2093815
zbMATH Keywords: nonlinear difference equation
zbMATH Keywords: positive solution
zbMATH Keywords: periodic solution
author: Hristo Voulov
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.02.054
OpenAlex ID: W1984935819
cites work: Q4390719
cites work: A difference equation with eventually periodic solutions
cites work: A reciprocal difference equation with maximum
cites work: On the Periodic Character of Some Difference Equations
cites work: Q4938118
cites work: Eventually periodic solutions of \(x_{n+1}=\max\{1/x_ n,A_ n/x_{n-1}\}\).
cites work: On \(x_{n+1}=\max \{\frac{1}{x_n},\frac{A_n}{x_{n-1}}\}\) with a period 3 parameter
cites work: Q4465349
DOI: 10.1016/J.JMAA.2004.02.054
description: scientific article; zbMATH DE number 2093815