On the location of zeroes of oscillatory solutions of \(y^{(n)}=c(x)y\)
type: Item
instance of: scholarly article
title: On the location of zeroes of oscillatory solutions of \(y^{(n)}=c(x)y\)
zbMATH Open document ID: 0554.34020
author: D. Kharzeev
published in: Pacific Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: It is known that the location of zeroes of solutions of differential equations is important to the study of certain boundary value problems and to certain eigenvalue problems. The location of zeroes of solutions of wide classes of differential equations \(y^{(n)}=c(x)y\) is obtained on an infinite interval. The structure of the subspaces of oscillatory solutions is given in detail. This leads to oscillation and nonoscillation criteria. Prufer type representations are produced for this high order differential equation. Asymptotic techniques are used. The finer asymptotic behaviour of solutions and their derivatives up to the n-th order is revealed. The usefulness of the definition ''almost diagonal systems'' is demonstrated.
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 3882765
zbMATH Keywords: location of zeroes of solutions
zbMATH Keywords: oscillatory solutions
zbMATH Keywords: asymptotic techniques
zbMATH Keywords: almost diagonal systems
MaRDI profile type: Publication
full work available at URL: pjm.1985.119.317
OpenAlex ID: W2008247575
DOI: 10.2140/PJM.1985.119.317
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description: scientific article; zbMATH DE number 3882765