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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 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
Email: mjhuang@math.nthu.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05015-7
PII: S 0002-9939(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