An oscillation test for a class of linear neutral differential equations
type: Item
instance of: scholarly article
title: An oscillation test for a class of linear neutral differential equations
zbMATH Open document ID: 0731.34090
DOI: 10.1016/0022-247X(91)90204-D
author: Jaroslav Jaroš
published in: Journal of Mathematical Analysis and Applications
publication date: 1991-01-01T00:00:00Z
review text: The author concerns with the problem of oscillation of the first-order neutral differential equations of the form \[ (A_ j)\quad \frac{d}{dt}[x(t)-h(t)x(\tau (t))]+(-1)^ jp(t)x(g(t))=0\quad (j=1,2), \] where h and \(p:[t_ 0<\infty)\to (0,\infty)\) are continuous, \(\tau\) and g: [t\({}_ 0,\infty)\to R\) are continuous, \(\tau\) is an increasing function, and \(\lim_{t\to \infty}\tau (t)=\infty\), \(\lim_{t\to \infty}g(t)=\infty.\) First, the author shows that the possible non-oscillatory solutions of \((A_ 2)\) (or \((A_ 1))\) can be partitioned into disjoint subsets \(N^+\) and \(N^-\) of the set N of all non-oscillatory solutions according to whether \[ (1)\quad x(t)y(t)>0\quad or \] \[ (2)\quad x(t)y(t)<0\quad (y(t)=x(t)-h(t)x(\tau (t))). \] The main results of this paper establish the nonexistence of non-oscillatory solutions of \((A_ j)\) \((j=1,2)\) satisfying (1) or (2). Combining these results, the sufficient conditions for all proper solutions of \((A_ 2)\) (or \((A_ 1))\) to be oscillatory are presented.
Mathematics Subject Classification ID: 34K40
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34K99
zbMATH DE Number: 4208606
zbMATH Keywords: problem of oscillation
zbMATH Keywords: first-order neutral differential equations
reviewed by: Jan Ohriska
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4208606