Stability properties of nonlinear difference equations and conditions for boundedness
type: Item
instance of: scholarly article
title: Stability properties of nonlinear difference equations and conditions for boundedness
zbMATH Open document ID: 0936.39004
DOI: 10.1016/S0898-1221(99)00179-0
author: Long-Tu Li
publication date: 2000-01-20T00:00:00Z
review text: The paper deals with a difference equation of the form \[ x_{n+1}=f(x_n)g(x_{n-k}),\quad n = 0, 1,\dots \tag{1} \] with positive initial conditions where \(f, g \in C([0,\infty), [0, \infty))\), \(f\) is increasing, \(g\) is decreasing, and the equation \(x=f(x)g(x)\) has a unique positive solution. Sufficient conditions for the global asymptotic stability and boundedness of solutions of equation (1) are obtained. As an application, the rational recursive sequence \(x_{n+1}=(a+bx_n^2)/(c+x_{n-k}^2)\), \(n=0,1,\dots\), where \(a,b,c\in(0,\infty)\), \(k\in \{1,2,\dots\}\) is considered.
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 1391611
zbMATH Keywords: nonlinear difference equations
zbMATH Keywords: global asymptotic stability
zbMATH Keywords: boundedness
zbMATH Keywords: positive solution
reviewed by: Victor I. Tkachenko
MaRDI profile type: Publication
cites work: Q3137926
cites work: Monotone unstable solutions of difference equations and conditions for boundedness
cites work: Permanence Of
cites work: A delayed-recruitment model of population dynamics, with an application to baleen whale populations
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 1391611