Oscillatory and nonoscillatory delay equations with piecewise constant argument
type: Item
instance of: scholarly article
title: Oscillatory and nonoscillatory delay equations with piecewise constant argument
zbMATH Open document ID: 0966.34063
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-08-08T00:00:00Z
review text: The authors consider the linear delay differential equation with piecewise constant deviating argument of the form \[ y'(t)+ a(t)y(t)+b(t)y([t-1])=0,\quad t\geq 0, \tag{1} \] where \(a(t),\;b(t)\) are continuous functions on \([-1,\infty),\;b(t)\geq 0(\not\equiv 0)\) for \(t\geq 0\), and \([\cdot ]\) denotes the greatest integer function. A new technique to analyze certain difference equations to obtain some new oscillation and nonoscillation criteria for equation (1) is introduced. Moreover, the authors prove that equation (1) can be classified as oscillatory or nonoscillatory, i.e., either all solutions are oscillatory or all solutions are nonoscillatory. The authors emphasize that their method yields ``best possible'' oscillation and nonoscillation criteria.
reviewed by: Jan Ohriska
Mathematics Subject Classification ID: 34K11
zbMATH DE Number: 1523544
zbMATH Keywords: oscillation theory
zbMATH Keywords: linear functional-differential equations
author: Jianhua Shen
author: Ioannis P. Stavroulakis
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6908
OpenAlex ID: W2087528268
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DOI: 10.1006/JMAA.2000.6908
description: scientific article; zbMATH DE number 1523544