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The difference of consecutive eigenvalues

Part of: Spectral theory and eigenvalue problems

Published online by Cambridge University Press:  09 April 2009

Hsu-Tung Ku  and
Mei-Chin Ku
Hsu-Tung Ku
Affiliation:
Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003, USA
Mei-Chin Ku
Affiliation:
Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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Abstract

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Let M be a smooth bounded domain in Rn with smooth boundary, n ≥ 2, and . We prove an inequality involving the first k + 1 eigenvalues of the eigenvalue problem: where am−1 ≥ 0 are constants and at−1 = 1. We also obtain a uniform estimate of the upper bound of the ratios of consecutive eigenvalues.

MSC classification

Secondary: 35P15: Estimation of eigenvalues, upper and lower bounds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 3 , December 1994 , pp. 305 - 315
Copyright
Copyright © Australian Mathematical Society 1994

References

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