Oscillatory properties of second order nonlinear differential equations
type: Item
instance of: scholarly article
title: Oscillatory properties of second order nonlinear differential equations
zbMATH Open document ID: 1205.34034
DOI: 10.1216/RMJ-2010-40-2-445
published in: Rocky Mountain Journal of Mathematics
publication date: 2010-06-14T00:00:00Z
review text: The authors derive necessary and sufficient criteria for the oscillation, nonoscilation, and strong oscillation of the second order nonlinear differential equation \[ u''+f(t,u,u')=0 \] on \([a,\infty)\), where \(f:[a,\infty)\times{\mathbb R}^2\to{\mathbb R}\) is continuous and \(f(t,x,y)\geq0\) on \([a,\infty)\times{\mathbb R}^2\). The results generalize several criteria known for the case of \(f(t,x,y)=h(t)\,g(x)\). The proofs involve, in particular, iterated exponential and logarithmic functions and the Kiguradze lemma. Several examples are also presented to illustrate the sharpness of the conditions.
reviewed by: Roman Šimon Hilscher
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 5720614
zbMATH Keywords: proper solution
zbMATH Keywords: oscillatory solution
zbMATH Keywords: non-oscillatory solution
zbMATH Keywords: oscillation criteria
zbMATH Keywords: non-oscillation criteria
author: Zuzana Došlá
author: Nino Partsvania
MaRDI profile type: Publication
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full work available at URL: rmj-2010-40-2-445
OpenAlex ID: W2000769410
description: scientific article; zbMATH DE number 5720614