Oscillation criteria for certain nonlinear differential equations
type: Item
instance of: scholarly article
title: Oscillation criteria for certain nonlinear differential equations
zbMATH Open document ID: 0921.34034
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-09-23T00:00:00Z
review text: The author studies the second-order ordinary differential equation \[ x''(t)+p(t)f(x(t))g(x'(t))=0,\tag{1} \] and the delay differential equations \[ x''(t)+p(t)f(x(\tau (t)))g(x'(t))=0\tag{2} \] and \[ x''(t)+p(t)f(x(t),x(\tau (t)))g(x'(t))=0 \tag{3} \] for \(t\geq t_0\). He obtains oscillation criteria for equations (1), (2) and (3), complements those given by \textit{S. R. Grace} and \textit{B. S. Lalli} [J. Math. Anal. Appl. 123, 584-588 (1987; Zbl 0641.34031)] and \textit{G.G. Hamedani and G.S. Krenz} [J. Math. Anal. Appl. 149, No. 1, 271-276 (1990; Zbl 0701.34043)] and handles the cases which are not covered by known criteria. The results are obtained by using an integral averaging technique.
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34C29
zbMATH DE Number: 1251422
zbMATH Keywords: oscillation theory
zbMATH Keywords: nonlinear oscillations
zbMATH Keywords: averaging method
author: Yuriy V. Rogovchenko
reviewed by: Jan Ohriska
MaRDI profile type: Publication
full work available at URL: jmaa.1998.6148
OpenAlex ID: W2038301884
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DOI: 10.1006/JMAA.1998.6148
description: scientific article; zbMATH DE number 1251422