On the ratio of the first two eigenvalues of perturbed harmonic oscillators

Journal of Mathematical Analysis and Applications

Volumn 204, Issue 1, 1996, Pages 227-235

  Kurata, Kazuhiro ^a  

^a NONE

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Indexed keywords

EID: 0030588763     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1996.0434     Document Type: Article

References (10)

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3. M. S. Ashbaugh and R. D. Benguria, A sharp bound for the ratio of the first two eigenvalues of Dirichlet Laplacians and extensions, Ann. of Math. 135 (1992), 601-628.
4. M. S. Ashbaugh and R. D. Benguria, On the ratio of the first two eigenvalues of Schrödinger operators with positive potentials, in "Proc., 1986 UAB/UA International Conference on Differential Equations and Mathematical Physics," Lecture Notes in Math, Vol. 1285, pp. 16-25. Springer-Verlag, New York/Berlin.
5. M. S. Ashbaugh and R. D. Benguria, Optimal lower bounds for eigenvalue gaps for Schrödinger operators with symmetric single-well potentials and related results, in "Maximum Principles and Eigenvalue Problems in Partial Differential Equations" (P. W. Schaefer, Ed.), Pitman Research Notes, Vol. 175, pp. 134-145, Pitman, Essex/New York, 1988.
6. M. S. Ashbaugh and R. D. Benguria, Optimal bounds for ratios of eigenvalues of one-dimensional Schrödinger operators with Dirichlet boundary conditions and positive potentials, Comm. Math. Phys. 124 (1989), 403-415.
7. 2 for the membrane problem, Duke Math. J. 63 (1991), 333-341.
8. E. M. Harrell II, General bounds for the eigenvalues of Schrödinger operators, in "Maximum Principles and Eigenvalue Problems in Partial Differential Equations" (P. W. Schaefer, Ed.), Pitman Research Notes, Vol. 175, pp. 146-166, Pitman, Essex/New York, 1988.
9. L. E. Payne, G. Pólya, and H. Weinberger, On the ratio of consecutive eigenvalues, J. Math. Phys. 35 (1956), 289-298.
10. M. Reed and B. Simon, "Methods of Modern Mathematical Physics," Vol. IV, "Analysis of Operators," Academic Press, New York, 1978.