Relative oscillation -- non-oscillation criteria for perturbed periodic Dirac systems
type: Item
instance of: scholarly article
title: Relative oscillation -- non-oscillation criteria for perturbed periodic Dirac systems
zbMATH Open document ID: 0977.34076
author: Karl Michael Schmidt
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-11-27T00:00:00Z
review text: The author considers radial Dirac operators and gives criteria on perturbations of the coefficients which ensure that the solutions to the perturbed problem are ``relatively nonoscillatory'' in the sense that the difference between the Prüfer angles of the solutions to the perturbed and unperturbed problems remains bounded. As an application, results of \textit{M. Klaus} [On the point spectrum of Dirac operators, Helv. Phys. Acta 53, No. 3, 453-462 (1980)] on the finiteness of the number of eigenvalues for the potential \(-c/(1+r^2)\), \(0<c<1/8\), are extended to the borderline case \(c=1/8\) [see also \textit{M. Griesemer} and \textit{J. Lutgen}, J. Funct. Anal. 162, No. 1, 120-134 (1999; Zbl 0926.34074)]. The argument leans on previous work by the author, especially [Commun. Math. Phys. 211, No. 2, 465-485 (2000; Zbl 0953.34069)].
reviewed by: Satyanad Kichenassamy
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 81Q05
zbMATH DE Number: 1496312
zbMATH Keywords: Dirac operator
zbMATH Keywords: radial solutions
zbMATH Keywords: nonoscillation criteria
zbMATH Keywords: eigenvalue estimates
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6821
OpenAlex ID: W2000458602
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DOI: 10.1006/JMAA.2000.6821
description: scientific article; zbMATH DE number 1496312