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Journal of Computational and Applied Mathematics
Volume 171, Issues 1-2, 1 October 2004, Pages 93-101
Special issue on the occasion of the eightieth birthday of Prof. W.M. Everitt
 
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doi:10.1016/j.cam.2004.01.015    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2004 Elsevier B.V. All rights reserved.

Oscillation results for Sturm–Liouville problems with an indefinite weight function

P. Bindinga, H. LangerCorresponding Author Contact Information, E-mail The Corresponding Author, b and M. Möllerc

a Department of Mathematics and Statistics, University of Calgary, Calgary AB, Canada T2N 1N4 b Institute of Analysis and Technical Mathematics, Vienna University of Technology, Wiedner Hauptstrasse 8–10, Vienna A-1040, Austria c School of Mathematics, University of the Witwatersrand, Johannesburg, 2050 WITS, South Africa

Received 18 June 2003. 
Available online 18 March 2004.

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Abstract

We prove oscillation results for the real eigenvalues of Sturm–Liouville problems with an indefinite weight function. An essential role is played by the signature of an eigenvalue, which is shown to be related to the signs of the corresponding leading coefficients of the Titchmarsh–Weyl m-function and of the Prüfer angle at this eigenvalue.

Author Keywords: Sturm Liouville operator; Indefinite weight; Oscillation theory; m-Function; Prüfer angle; Signature of an eigenvalue

Mathematical subject codes: primary 34B09; 34C10; 34B24; secondary 47B50

Article Outline

1. Introduction
2. Real eigenvalues and their signatures
3. The Titchmarsh–Weyl function and the Prüfer angle
4. Oscillation results
Acknowledgements
References

Journal of Computational and Applied Mathematics
Volume 171, Issues 1-2, 1 October 2004, Pages 93-101
Special issue on the occasion of the eightieth birthday of Prof. W.M. Everitt
 
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