Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the eigenvalue ratio for vibrating strings

Author: Min-Jei Huang
Journal: Proc. Amer. Math. Soc. 127 (1999), 1805-1813
MSC (1991): Primary 34L15
Published electronically: February 17, 1999
MathSciNet review: 1621941
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Abstract: For vibrating strings with concave densities or symmetric single-barrier densities, the ratio $\lambda _2/\lambda _1$ of the first two eigenvalues is minimized when the density is constant; while, for vibrating strings with symmetric single-well densities, the ratio $\lambda _2/\lambda _1$ 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

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