The first instability interval for Hill equations with symmetric single well potentials
HTML articles powered by AMS MathViewer
- by Min-Jei Huang PDF
- Proc. Amer. Math. Soc. 125 (1997), 775-778 Request permission
Abstract:
For Hill equations with symmetric single well (or symmetric single barrier) potentials, the first instability interval is absent when and only when the potential is constant.References
- M. S. Ashbaugh and R. Benguria, Optimal lower bounds for eigenvalue gaps for Schrödinger operators with symmetric single-well potentials and related results, Maximum principles and eigenvalue problems in partial differential equations (Knoxville, TN, 1987) Pitman Res. Notes Math. Ser., vol. 175, Longman Sci. Tech., Harlow, 1988, pp. 134–145. MR 963464
- Mark S. Ashbaugh and Rafael Benguria, Optimal lower bound for the gap between the first two eigenvalues of one-dimensional Schrödinger operators with symmetric single-well potentials, Proc. Amer. Math. Soc. 105 (1989), no. 2, 419–424. MR 942630, DOI 10.1090/S0002-9939-1989-0942630-X
- P. Erdös and T. Grünwald, On polynomials with only real roots, Ann. of Math. (2) 40 (1939), 537–548. MR 7, DOI 10.2307/1968938
- M. S. P. Eastham, The Spectral Theory of Periodic Differential Equations, Scottish Academic Press, Edinburgh and London, 1973.
- Harry Hochstadt, Functiontheoretic properties of the discriminant of Hill’s equation, Math. Z. 82 (1963), 237–242. MR 156022, DOI 10.1007/BF01111426
- Harry Hochstadt, On the determination of a Hill’s equation from its spectrum, Arch. Rational Mech. Anal. 19 (1965), 353–362. MR 181792, DOI 10.1007/BF00253484
- Harry Hochstadt, On a Hill’s equation with double eigenvalues, Proc. Amer. Math. Soc. 65 (1977), no. 2, 373–374. MR 445059, DOI 10.1090/S0002-9939-1977-0445059-8
- Richard Lavine, The eigenvalue gap for one-dimensional convex potentials, Proc. Amer. Math. Soc. 121 (1994), no. 3, 815–821. MR 1185270, DOI 10.1090/S0002-9939-1994-1185270-4
- Wilhelm Magnus and Stanley Winkler, Hill’s equation, Interscience Tracts in Pure and Applied Mathematics, No. 20, Interscience Publishers John Wiley & Sons, New York-London-Sydney, 1966. MR 0197830
- Peter Ungar, Stable Hill equations, Comm. Pure Appl. Math. 14 (1961), 707–710. MR 176148, DOI 10.1002/cpa.3160140403
Additional Information
- Min-Jei Huang
- Affiliation: Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 30043
- Email: mjhuang@math.nthu.edu.tw
- Received by editor(s): July 10, 1995
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 775-778
- MSC (1991): Primary 34B30, 34L15
- DOI: https://doi.org/10.1090/S0002-9939-97-03705-2
- MathSciNet review: 1363425