A class of first-order nonlinear difference equations of neutral type
type: Item
instance of: scholarly article
title: A class of first-order nonlinear difference equations of neutral type
zbMATH Open document ID: 1066.39011
author: Małgorzata Migda
author: Janusz Migda
published in: Mathematical and Computer Modelling
publication date: 2005-02-22T00:00:00Z
review text: The authors classify all nonoscillatory solutions and find criteria for oscillation of all solutions of the first order nonlinear difference equations of neutral type \[ \Delta\Big(x(n)-p(n)x\big(\tau(n)\big)\Big)+ \delta\sum_{j=1}^nq_j(n)f_j\Big(x\big(\sigma_j(n)\big)\Big)=0, \] where \(\delta=\pm 1\), \(f_j:{\mathbb R}\to{\mathbb R}\), and for \({\mathbb N}(n_0)=\{n_0,n_0+1,\dots\}\), \(p,q_j:{\mathbb N}(n_0)\to{\mathbb R}_+\), \(\tau,\sigma_j:{\mathbb N}(n_0)\to{\mathbb N}\), and \(\lim\limits_{n\to\infty}\tau(n)=\infty\), \(\lim\limits_{n\to\infty}\sigma_j(n)=\infty\) for all \(j\in\{1,\dots,n\}\).
reviewed by: Oleksiy Karlovych
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 2137078
zbMATH Keywords: first-order nonlinear difference equations of neutral type
zbMATH Keywords: nonoscillatory solution
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: oscillation
MaRDI profile type: Publication
full work available at URL: j.mcm.2003.12.006
OpenAlex ID: W2047451263
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DOI: 10.1016/J.MCM.2003.12.006
description: scientific article; zbMATH DE number 2137078