Asymptotic behaviour of the maxima of solutions of certain differential equations
type: Item
instance of: scholarly article
title: Asymptotic behaviour of the maxima of solutions of certain differential equations
zbMATH Open document ID: 0924.34028
author: Gerd Herzog
author: Ray Redheffer
published in: Archiv der Mathematik
publication date: 1999-06-30T00:00:00Z
review text: The differential equation \(u''+qu=0\) is said to have the Wintner property if for all solutions the relative maxima of \(q^{1/4}| u |\) converge to a finite positive limit as \(t\to\infty\). Some new methods are described by which the Wintner property may be established in certain cases. On the other hand, the authors show that this property is exceptional: the set of \(q\) for which the equation has the Wintner property is residual in the sense of Baire category.
reviewed by: Erhard Heil
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 1295484
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: maxima of solutions
zbMATH Keywords: oscillation
zbMATH Keywords: Wintner property
MaRDI profile type: Publication
full work available at URL: s000130050314
OpenAlex ID: W2066376356
DOI: 10.1007/S000130050314
description: scientific article; zbMATH DE number 1295484