Some notes on ``Oscillatory and asymptotic behaviour of second order nonlinear difference equations''
type: Item
instance of: scholarly article
title: Some notes on ``Oscillatory and asymptotic behaviour of second order nonlinear difference equations''
zbMATH Open document ID: 0816.39001
author: Xingbao Wu
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-07-20T00:00:00Z
review text: \textit{X. He} [ibid. 175, No. 2, 482-498 (1993; Zbl 0780.39001)] asserted that if \(\{x_ n\}\) is a nontrivial solution of the second order nonlinear difference equation \(\Delta (r_ n \Delta x_ n) + f(n,x_ n) = 0\) such that \(x_ n f(n, x_ n) \leq 0\) for all \(n\) large, then \(\{x_ n\}\) must be nonoscillatory. One can easily see by means of counterexamples that this conclusion is wrong.
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 743900
zbMATH Keywords: second order nonlinear difference equation
zbMATH Keywords: counterexamples
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1018
OpenAlex ID: W2036747020
DOI: 10.1006/JMAA.1995.1018
description: scientific article; zbMATH DE number 743900