Lower order eigenvalues of the Schrodinger operator

Authors

  • Bingqing Ma Department of Mathematics, Henan Normal University, Xinxiang 453007, Henan, People's Republic of China

DOI:

https://doi.org/10.26713/cma.v5i2.176

Keywords:

Membrane eigenvalue, Schrodinger operator, Rayleigh-Ritz inequality

Abstract

Making use of the method introduced by Brands in [4], we consider lower order eigenvalues of the Schrodinger operator in Euclidean domains. We extend an estimate on eigenvalues obtained by Ashbaugh and Benguria in [3].

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References

H. J. Sun, Q. M. Cheng and H. C. Yang, Lower order eigenvalues of Dirichlet Laplacian, Manuscripta Math., 125 (2008), 139-156.

L. E. Payne, G. Polya and H. F. Weinberger, On the ratio of consecutive eigenvalues, J. Math. Phys., 35 (1956), 289-298.

M. S. Ashbaugh and R. D. Benguria, More bounds on eigenvalue ratios for Dirichlet Laplacians in n dimensions, SIAM J. Math. Anal., 24 (1993), 1622-1651.

J. J. A. M. Brands, Bounds for the ratios of the first three membrane eigenvalues, Arch. Rational Mech. Anal., 16 (1964), 265-268.

D. G. Chen and Q. M. Cheng, Extrinsic estimates for eigenvalues of the Laplace operator, J. Math. Soc. Japan, 60 (2008), 325-339.

G. Y. Huang, X. X. Li and R. W. Xu, Extrinsic estimates for the eigenvalues of Schrí„odinger operator, Geom. Dedicata, 143 (2009), 89-107.

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Published

30-10-2014
CITATION

How to Cite

Ma, B. (2014). Lower order eigenvalues of the Schrodinger operator. Communications in Mathematics and Applications, 5(2), 47–52. https://doi.org/10.26713/cma.v5i2.176

Issue

Vol. 5 No. 2 (2014)

Section

Research Article

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