Asymptotic behavior of solutions for a class of difference equations
type: Item
instance of: scholarly article
title: Asymptotic behavior of solutions for a class of difference equations
zbMATH Open document ID: 0874.39009
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-11-11T00:00:00Z
review text: Let the functions \(F\), \(G\in C(\mathbb{R},\mathbb{R})\) and let \(F\) be increasing. If \(F(y)\geq G(y)\) \([F(y)\leq G(y)]\) for all \(y\in\mathbb{R}\), then each solution of the nonlinear difference equation \[ x_n-x_{n-1}=-F(x_n)+G(x_{n-k}),\quad n\geq n_0, \] with positive integer \(k\), tends to either a constant or \(-\infty\) \([+\infty]\) as \(n\to\infty\). Some illustrative examples are included.
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 1005602
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: nonlinear difference equation
author: Lihong Huang
author: Jianshe Yu
reviewed by: Dobiesław Bobrowski
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0470
OpenAlex ID: W2077503783
DOI: 10.1006/JMAA.1996.0470
description: scientific article; zbMATH DE number 1005602