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shrinking domains

Proceedings of the Edinburgh Mathematical Society (1)

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ON THE BEHAVIOUR OF EIGENVALUES ASSOCIATED WITH STURM–LIOUVILLE PROBLEMS ON SHRINKING DOMAINS
D. J. Needham, A. C. King
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Proceedings of the Edinburgh Mathematical Society / Volume 49 / Issue 1 / February 2006

Published online by Cambridge University Press:

02 February 2006, pp. 201-214
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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.