Lower order eigenvalues of the Schrodinger operator

Bingqing Ma

doi:10.26713/cma.v5i2.176

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].

804 209

Downloads

Download data is not yet available.

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.