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ON THE BEHAVIOUR OF EIGENVALUES ASSOCIATED WITH STURM–LIOUVILLE PROBLEMS ON SHRINKING DOMAINS

Published online by Cambridge University Press:  02 February 2006

D. J. Needham  and
A. C. King
D. J. Needham
Affiliation:
Department of Mathematics, University of Reading, PO Box 220, Reading RG6 6AX, UK (d.j.needham@reading.ac.uk)
A. C. King
Affiliation:
Department of Mathematics, University of Reading, PO Box 220, Reading RG6 6AX, UK (d.j.needham@reading.ac.uk)
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Abstract

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We establish results concerning the detailed asymptotic structure of the eigenvalues of a class of regular and singular Sturm–Liouville problems as the domain size shrinks to zero. This is motivated by the recent paper of Bailey et al. and provides an extensive generalization of the results therein.

Keywords

Primary 34B24Sturm–Liouville eigenvalue problemshrinking domainsasymptotic behaviour
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 49 , Issue 1 , February 2006 , pp. 201 - 214
Copyright
Copyright © Edinburgh Mathematical Society 2006