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Eigenvalue ratios and eigenvalue gaps of Sturm–Liouville operators

Published online by Cambridge University Press:  14 November 2011

C. K. Law  and
Yu-Ling Huang
C. K. Law
Affiliation:
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan 80424, R.O.C., E-mail: law@sunl.math.nsysu.edu.tw
Yu-Ling Huang
Affiliation:
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan 80424, R.O.C
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Abstract

We prove optimal lower bounds for arbitrary eigenvalue ratios (μm/μn) of the Sturm–Liouville operator with Dirichlet and Neumann boundary conditions. These imply optimal bounds for the eigenvalue gaps (μm – μn) of the corresponding problem. The method can be generalised to consider general separated endpoint boundary conditions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 2 , 1998 , pp. 337 - 347
Copyright
Copyright © Royal Society of Edinburgh 1998

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