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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the first two eigenvalues of Sturm-Liouville operators


Author: Miklós Horváth
Journal: Proc. Amer. Math. Soc. 131 (2003), 1215-1224
MSC (2000): Primary 34L15, 34B25
Published electronically: July 26, 2002
MathSciNet review: 1948113
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Abstract: Among the Schrödinger operators with single-well potentials defined on $(0,\pi)$ with transition point at $\frac\pi 2$, the gap between the first two eigenvalues of the Dirichlet problem is minimized when the potential is constant. This extends former results of Ashbaugh and Benguria with symmetric single-well potentials. An analogous result is given for the Dirichlet problem of vibrating strings with single-barrier densities for the ratio of the first two eigenvalues.


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Additional Information

Miklós Horváth
Affiliation: Department for Mathematical Analysis, Institute of Mathematics, Technical University of Budapest, H 1111 Budapest, Műegyetem rkp. 3-9, Hungary
Email: horvath@math.bme.hu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06637-6
PII: S 0002-9939(02)06637-6
Received by editor(s): July 25, 2001
Received by editor(s) in revised form: November 18, 2001
Published electronically: July 26, 2002
Additional Notes: Supported by the Hungarian Grant OTKA T032374
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2002 American Mathematical Society