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An oscillation theorem for self-adjoint differential systems and an index result for corresponding Riccati matrix differential equations

Published online by Cambridge University Press:  24 October 2008

Werner Kratz
Werner Kratz
Affiliation:
Abteilung Mathematik V, Universität Ulm, D-89069 Ulm, Germany e-mail: [email protected]
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Abstract

The main result of this paper is an oscillation theorem on linear self-adjoint differential systems and a corresponding eigenvalue problem. It establishes a formula between the number of focal points of a so-called conjoined basis of the differential system on a given compact interval and the number of eigenvalues which are less than the given eigenvalue parameter. It extends an earlier result of the author and generalizes an oscillation theorem of M. Morse. Among others the proof of the theorem requires a formula on the index of the difference of symmetric solutions of a corresponding Riccati matrix differential equation. This index formula is the other new result presented.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 2 , September 1995 , pp. 351 - 361
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

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