Taiwanese Journal of Mathematics

OPTIMAL LOWER ESTIMATES FOR EIGENVALUE RATIOS OF SCHRÖDINGER OPERATORS AND VIBRATING STRINGS

Chung-Chuan Chen, C. K. Law, and F. Y. Sing

Full-text: Open access

Abstract

We obtain optimal lower estimates for the eigenvalue ratios $(\frac{\lambda_{m}}{\lambda_{n}})$ of Dirichlet and Neumann Schrödinger operators with nonpositive potentials and Dirichlet vibrating string problems with concave and positive densities. Our results supplement those of Ashbaugh-Benguria [2] and M. J. Huang [5].

Article information

Source
Taiwanese J. Math., Volume 9, Number 2 (2005), 175-185.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500407794

Digital Object Identifier
doi:10.11650/twjm/1500407794

Mathematical Reviews number (MathSciNet)
MR2142571

Zentralblatt MATH identifier
1086.34069

Subjects
Primary: 34B24: Sturm-Liouville theory [See also 34Lxx] 34L15: Eigenvalues, estimation of eigenvalues, upper and lower bounds

Keywords
Schrödinger operators vibrating string problems eigenvalue ratios modified Prüfer substitution

Citation

Chen, Chung-Chuan; Law, C. K.; Sing, F. Y. OPTIMAL LOWER ESTIMATES FOR EIGENVALUE RATIOS OF SCHRÖDINGER OPERATORS AND VIBRATING STRINGS. Taiwanese J. Math. 9 (2005), no. 2, 175--185. doi:10.11650/twjm/1500407794. https://projecteuclid.org/euclid.twjm/1500407794


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References

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