Oscillations of higher-order neutral difference equations
type: Item
instance of: scholarly article
title: Oscillations of higher-order neutral difference equations
zbMATH Open document ID: 0890.39019
DOI: 10.1016/S0893-9659(96)00114-0
published in: Applied Mathematics Letters
publication date: 1998-06-28T00:00:00Z
review text: The authors investigate the oscillatory behavior of the solutions of an order \(m\) nonlinear neutral difference equation of the form \[ \Delta^m(y_n+p_ny_{n-k})+q_nf(y_{n-l})=0,\quad n\in\mathbb{N}=\{0,1,\ldots\}, \] where \(\Delta\) is the usual forward difference operator defined by \(\Delta y_n=y_{n+1}-y_n\), \(k\), \(l\) are nonnegative integers, \(\{p_n\}\), \(\{q_n\}\) are real sequences with \(q_n\geq 0\), \(n\in\mathbb{N}\), and \(f:\mathbb{R}\to\mathbb{R}\) is continuous with \(uf(u)>0\), for all \(u\neq 0\). Some sufficient conditions are given which ensure that all solutions of the above equation are oscillatory.
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 1078539
zbMATH Keywords: nonlinear neutral difference equation
zbMATH Keywords: oscillatory solutions
author: Ravi P. Agarwal
author: E. Thandapani
author: Patricia J. Y. Wong
reviewed by: Alexander Mednykh
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1078539