Oscillatory behavior of \(n^{th}\)-order neutral differential equations with continuous deviating arguments
type: Item
instance of: scholarly article
title: Oscillatory behavior of \(n^{th}\)-order neutral differential equations with continuous deviating arguments
zbMATH Open document ID: 1076.34077
author: R. S. Dahiya
published in: Mathematical and Computer Modelling
publication date: 2005-05-12T00:00:00Z
review text: The paper deals with the \(n\)th-order neutral functional-differential equation \[ [a(t)[x(t)| x(t)|^{\alpha-1}+p(t)x(\tau(t))]^{(n-1)}]'+\delta\int_c^d q(t,\xi)f(x(\sigma(t,\xi)))\,d\xi =h(t),\tag{1} \] with \(\delta=\pm 1\), \(t\geq 0\). The author presents sufficient conditions for equation (1) to be almost oscillatory in the sense that every solution \(x(t)\) of this equation is either oscillatory or else \(\lim_{t\to\infty}| x(t)| =\infty\), or \(\liminf_{t\to\infty}| x(t)| =0\). Two examples are given for illustration.
reviewed by: Jan Ohriska
Mathematics Subject Classification ID: 34K11
Mathematics Subject Classification ID: 34K40
zbMATH DE Number: 2167467
zbMATH Keywords: neutral equations
zbMATH Keywords: oscillation theory
MaRDI profile type: Publication
full work available at URL: j.mcm.2003.06.008
OpenAlex ID: W2050489914
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DOI: 10.1016/J.MCM.2003.06.008
description: scientific article; zbMATH DE number 2167467