Oscillation of higher-order neutral nonlinear difference equations
type: Item
instance of: scholarly article
title: Oscillation of higher-order neutral nonlinear difference equations
zbMATH Open document ID: 0946.39002
DOI: 10.1016/S0893-9659(98)00047-0
published in: Applied Mathematics Letters
publication date: 2000-10-12T00:00:00Z
review text: The paper deals with the higher-order neutral nonlinear difference equation \[ \Delta(r_n(\Delta^d (x_n - p_n x_{n-r}))^{\delta}) + f(n, x_{n-\sigma}) = 0, \tag{1} \] where \(n \in \{ n_0+1, n_0+2,...\}, n_0\) and \(\sigma\) are nonnegative integers, \(\tau\) and \(d\) are positive integers, \(\Delta x_n = x_{n+1} - x_n,\) \(\delta\) is a quotient of odd positive integers, \(0 \leq p_n < 1, r_n > 0,\) and \(f\) is continuous in \(x\) for \(x \in \mathbb{R}.\) A solution of (1) is called nonoscillatory if it is eventually positive or eventually negative. Some necessary and sufficient conditions for the existence of nonoscillatory solutions to (1) are obtained. The author gives necessary and sufficient conditions for all bounded solutions to (1) to be oscillatory or to tend to zero.
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 1369514
zbMATH Keywords: nonlinear neutral difference equation
zbMATH Keywords: oscillation
zbMATH Keywords: nonoscillatory solutions
zbMATH Keywords: bounded solution
author: Wan-Tong Li
reviewed by: Victor I. Tkachenko
MaRDI profile type: Publication
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full work available at URL: s0893-9659(98)00047-0
OpenAlex ID: W2060312770
description: scientific article; zbMATH DE number 1369514