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11.— A Left Definite Multiparameter Eigenvalue Problem in Ordinary Differential Equations*

Published online by Cambridge University Press:  14 February 2012

A. Källström  and
B. D. Sleeman
A. Källström
Affiliation:
Department of Mathematics, University of Dundee.
B. D. Sleeman
Affiliation:
Department of Mathematics, University of Dundee.
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Synopsis

The main result of this paper is to establish the completeness of the eigenfunctions for the multiparameter eigenvalue problem defined by the system of ordinary differential equations

0 ≤ x, ≤ 1, r = 1, …, k, subject to the Sturm-Liouville boundary conditions

r = 1, …, k. In addition it is assumed that the coefficients ars of the spectral parameters λs, satisfy the ellipticity condition , s = 1, …, k, for all xrɛ[0, 1], r = 1, …, k, and some real k-tuple μ1, …, μk and where is the co-factor of asr in the determinant . The theory developed here contrasts with the results known when …k is assumed non-vanishing for all xrɛ[0,1].

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 74 , 1976 , pp. 145 - 155
Copyright
Copyright © Royal Society of Edinburgh 1976

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References

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