Oscillation of second order unstable neutral difference equations with continuous arguments
type: Item
instance of: scholarly article
title: Oscillation of second order unstable neutral difference equations with continuous arguments
zbMATH Open document ID: 1087.39016
DOI: 10.1007/BF02831944
author: Yu Tian
author: Zhenguo Zhang
author: Weigao Ge
published in: Journal of Applied Mathematics and Computing
publication date: 2006-02-20T00:00:00Z
review text: Various conditions for oscillatory behavior of the bounded solutions of \[ \Delta^2_\tau(x(t)-px(t-\sigma))=f(t,x(g(t))) \] are given. Here \(\tau>0\), \(\sigma\in \mathbb R\), \(f(t,u)/u\geq q(t)>0\), \(q\in C((t_0,\infty),\mathbb R_+)\), \(g\in C^1((t_0,\infty),\mathbb R_+)\),\(0<g(t)<t\), \(\liminf_{t\rightarrow\infty}(g(t+\tau)-g(t))>\tau\), \(\Delta_\tau(x(t))=x(t+\tau)-x(t)\). The oscillatory behavior is valid for all bounded solutions of the equation and for \(0\leq p<1\), \(p=1\), \(p<0\), \(p>0\) respectively. The criteria are expressed in terms of equations coefficients via various iterated integral transformations.
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 34K40
zbMATH DE Number: 5007517
zbMATH Keywords: oscillatory behavior
zbMATH Keywords: continuous time
zbMATH Keywords: bounded solutions
reviewed by: Vladimir Răsvan
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02831944
OpenAlex ID: W1967972495
description: scientific article; zbMATH DE number 5007517