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On the first two eigenvalues of Sturm-Liouville operators
Author(s):
Miklós
Horváth
Journal:
Proc. Amer. Math. Soc.
131
(2003),
1215-1224.
MSC (2000):
Primary 34L15, 34B25
Posted:
July 26, 2002
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Abstract:
Among the Schrödinger operators with single-well potentials defined on  with transition point at  , 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, Muegyetem rkp. 3-9, Hungary
Email:
horvath@math.bme.hu
DOI:
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
Posted:
July 26, 2002
Additional Notes:
Supported by the Hungarian Grant OTKA T032374
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2002,
American Mathematical Society
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