Linearized oscillations in nonlinear delay difference equations
type: Item
instance of: scholarly article
title: Linearized oscillations in nonlinear delay difference equations
zbMATH Open document ID: 0939.39011
author: Sanyi Tang
author: Yanni Xiao
author: Jufang Chen
publication date: 2000-06-13T00:00:00Z
review text: Consider the nonlinear difference equation \[ x_{n+1}-x_n=\sum^m_{j=1} p_jf_j(x_{n-k_j})=0,\quad n\geq n_0\geq 0\tag{*} \] and its linearized version \[ x_{n+1}-x_n+\sum^m_{i=1} p_jx_{n-k_i}=0,\quad n\geq n_0,\tag{**} \] where \(n_0\in\{0,1,2,\dots\}\). If \(p_j>0\), \(k_j=0,1,2,\dots\), \(f_j\in C(\mathbb{R},\mathbb{R}]\), \(u\cdot f_j(u)>0\) (\(u\neq 0\)), \(u\in(-\alpha,\alpha)\) and \(\lim u^{-1}f_j(u)=1\) for all \(j=1,2,\dots,m\), then every solution of (**) is oscillatory if and only if (*) oscillates.
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 1385074
zbMATH Keywords: linearized oscillations
zbMATH Keywords: nonlinear delay difference equations
zbMATH Keywords: oscillatory solution
zbMATH Keywords: Schauder fixed point theorem
reviewed by: Dobiesław Bobrowski
MaRDI profile type: Publication
full work available at URL: s10114-999-0089-x
OpenAlex ID: W1982974320
cites work: Oscillation and comparison results for delay difference equations
cites work: Explicit conditions for the oscillation of difference equations
DOI: 10.1007/S10114-999-0089-X
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1385074