Oscillatory behaviour of a higher-order nonlinear neutral type functional difference equation with oscillating coefficients.
type: Item
instance of: scholarly article
title: Oscillatory behaviour of a higher-order nonlinear neutral type functional difference equation with oscillating coefficients.
zbMATH Open document ID: 1069.39007
published in: Applied Mathematics Letters
publication date: 2005-03-07T00:00:00Z
review text: The authors study the oscillatory behaviour of the higher-order nonlinear difference equation of the form: \[ \Delta^n[y(k)+p(k)y(k-\tau)]+q(k)f(y(\sigma(k)))=0, \] \(n\geq 2\), \(n,k\in\mathbb{N}\); \(p(k): \mathbb N\to \mathbb{R}\) is an oscillating function; \(q(k):\mathbb{N}\to[0,+\infty)\); \(\tau\) is a positive integer, \(\sigma(k):\mathbb{N}\to\mathbb{Z}\) with \(\sigma(k)\leq k\) and \(\sigma(k)\to\infty\) as \(k\to\infty\); \(f(u)\in C(\mathbb{R},\mathbb{R})\) is a nondecreasing function, \(uf(u)>0\) for \(u\neq 0\). Two sufficient criteria are obtained.
reviewed by: Costică Moroşanu
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 2140785
zbMATH Keywords: higher-order nonlinear neutral difference equations
zbMATH Keywords: oscillation
zbMATH Keywords: oscillating coefficients
author: Yaşar Bolat
author: Ömer Akın
MaRDI profile type: Publication
full work available at URL: j.aml.2004.07.011
OpenAlex ID: W1992067748
cites work: Q4502956
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cites work: Theory of difference equations: Numerical methods and applications
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cites work: Oscillatory behavior of higher order nonlinear neutral difference equation
DOI: 10.1016/J.AML.2004.07.011
description: scientific article; zbMATH DE number 2140785