On the eigenvalue ratio for vibrating strings

Huang, Min-Jei

doi:10.1090/S0002-9939-99-05015-7

On the eigenvalue ratio for vibrating strings
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Proc. Amer. Math. Soc. 127 (1999), 1805-1813 Request permission

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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