On the eigenvalue ratio for vibrating strings

Author:
Min-Jei Huang

Journal:
Proc. Amer. Math. Soc. **127** (1999), 1805-1813

MSC (1991):
Primary 34L15

DOI:
https://doi.org/10.1090/S0002-9939-99-05015-7

Published electronically:
February 17, 1999

MathSciNet review:
1621941

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Abstract | References | Similar Articles | Additional Information

Abstract: For vibrating strings with concave densities or symmetric single-barrier densities, the ratio of the first two eigenvalues is minimized when the density is constant; while, for vibrating strings with symmetric single-well densities, the ratio is maximized when the density is constant.

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Additional Information

**Min-Jei Huang**

Affiliation:
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 30043

Email:
mjhuang@math.nthu.edu.tw

DOI:
https://doi.org/10.1090/S0002-9939-99-05015-7

Keywords:
Eigenvalue ratio,
eigenfunction,
concave density,
symmetric single-well density

Received by editor(s):
September 19, 1997

Published electronically:
February 17, 1999

Communicated by:
Hal L. Smith

Article copyright:
© Copyright 1999
American Mathematical Society