Equivalence of oscillation of a class of neutral differential equations and ordinary differential equations
type: Item
instance of: scholarly article
title: Equivalence of oscillation of a class of neutral differential equations and ordinary differential equations
zbMATH Open document ID: 0883.34070
DOI: 10.4171/ZAA/772
author: Bo Yang
author: B. G. Zhang
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1998-02-23T00:00:00Z
review text: It is shown that a necessary and sufficient condition for equation \[ d/dt\left(x(t)-x(t-r )\right)^{(n)}+p(t)x(t-\sigma )=0,\tag{1} \] to oscillate is that the ordinary differential equation \[ x^{(n+1)}(t)+p(t)x(t)/r=0 \] is oscillatory. Here \(r>0\), \(\sigma \in \mathbb{R}\) are constants, \(n\geq 0\) is an odd integer and \(p:[0,\infty )\to [0,\infty )\) is a continuous function. Some comparison theorems are established. It is shown that the deviation \(\sigma\) has no affection on the oscillation of the equation (1).
Mathematics Subject Classification ID: 34K11
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34K40
zbMATH DE Number: 1045999
zbMATH Keywords: oscillation
zbMATH Keywords: positive solutions
zbMATH Keywords: neutral differential equations
reviewed by: Alexandra Rodkina
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1045999