On the first two eigenvalues of Sturm-Liouville operators
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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.References
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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
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1215-1224
- MSC (2000): Primary 34L15, 34B25
- DOI: https://doi.org/10.1090/S0002-9939-02-06637-6
- MathSciNet review: 1948113