On the positive solutions of the difference equation \(x_{n+1}=(x_{n-1})/(1+x_{n} x_{n-1})\).
type: Item
instance of: scholarly article
title: On the positive solutions of the difference equation \(x_{n+1}=(x_{n-1})/(1+x_{n} x_{n-1})\).
zbMATH Open document ID: 1050.39005
DOI: 10.1016/S0096-3003(03)00194-2
published in: Applied Mathematics and Computation
publication date: 2004-03-14T00:00:00Z
review text: The author obtains the exact expression of the positive solutions of the difference equation \[ x_{n+1}=\frac{x_{n-1}}{1+x_nx_{n-1}}, \quad n=0,1,2,\dots, \] where \(x_{-1}\) and \(x_0\) are two positive real numbers. From this expression it is deduced that the constant solution 0 is the unique equilibrium point.
reviewed by: Alberto Cabada
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A20
zbMATH DE Number: 2056325
zbMATH Keywords: difference equations
zbMATH Keywords: recursive sequence
zbMATH Keywords: positive solutions
zbMATH Keywords: equilibrium point
author: Cengiz Çinar
MaRDI profile type: Publication
cites work: A rational recursive sequence
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description: scientific article; zbMATH DE number 2056325