Eigenvalue ratios for the regular Sturm-Liouville system

Huang, Yu-Ling; Law, C.

doi:10.1090/S0002-9939-96-03396-5

Eigenvalue ratios for the regular Sturm-Liouville system
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by Yu-Ling Huang and C. K. Law PDF

Proc. Amer. Math. Soc. 124 (1996), 1427-1436 Request permission

Abstract:

Following the method of Ashbaugh-Benguria in Comm. Math. Phys. 124 (1989), 403–415; J. Differential Equations 103 (1993), 205–219, we prove an upper estimate of the arbitrary eigenvalue ratio $( \mu _m / \mu _n )$ for the regular Sturm-Liouville system. This upper estimate is sharp for Neumann boundary conditions. We also discuss the sign of $\mu _1$ and include an elementary proof of a useful trigonometric inequality first given in the aforementioned articles.

References

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