On positive solutions of a reciprocal difference equation with minimum
type: Item
instance of: scholarly article
title: On positive solutions of a reciprocal difference equation with minimum
zbMATH Open document ID: 1074.39002
DOI: 10.1007/BF02936057
author: Cengiz Çinar
author: Stevo Stević
author: İbrahim Yalçinkaya
published in: Journal of Applied Mathematics and Computing
publication date: 2005-03-10T00:00:00Z
review text: The authors consider the behavior of positive solutions of the equation \[ x_{n+1}=\min\left\{\frac{A}{x_{n}x_{n-1}\cdots x_{n-k}}, \frac{B}{x_{n-(k+2)}\cdots x_{n-(2k+2)}}\right\}, \;\;n\geq0, \] where \(A\), \(B\) and the initial values \(x_{-(2k+2)},\ldots,x_0\) are positive real numbers. It is shown that if \(0<A\leq B\) then all positive solutions are eventually periodic with period \(k+2\). A detailed study of the case \(k=0\) is presented.
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A20
zbMATH DE Number: 2143264
zbMATH Keywords: difference equation with minimum
zbMATH Keywords: periodic solution
zbMATH Keywords: positive solution
reviewed by: Oleg Anashkin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2143264