|
The first instability interval for Hill equations with symmetric single well potentials
Author(s):
Min-Jei
Huang
Journal:
Proc. Amer. Math. Soc.
125
(1997),
775-778.
MSC (1991):
Primary 34B30, 34L15
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
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:
- 1.
- M. 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 (P. W. Schaefer, ed.), Pitman Res. Notes Math. Ser., vol. 175, Longman Sci. Tech., Harlow, 1988, pp. 134-145. MR 90c:35157
- 2.
- -, 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), 419-424. MR 89f:81028
- 3.
- G. Borg, Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte, Acta Math. 78 (1946), 1-96. MR 7:382d
- 4.
- M. S. P. Eastham, The Spectral Theory of Periodic Differential Equations, Scottish Academic Press, Edinburgh and London, 1973.
- 5.
- H. Hochstadt, Functiontheoretic properties of the discriminant of Hill's equation, Math. Zeit. 82 (1963), 237-242. MR 27:5955
- 6.
- -, On the determination of a Hill's equation from its spectrum , Arch. Rational Mech. Anal. 19 (1965), 353-362; 23 (1966), 237-238. MR 31:6019; MR 34:411
- 7.
- -, On a Hill's equation with double eigenvalues, Proc. Amer. Math. Soc. 65 (1977), 373-374. MR 56:3404
- 8.
- R. Lavine, The eigenvalue gap for one-dimensional convex potentials, Proc. Amer. Math. Soc. 121 (1994), 815-821. MR 94i:35144
- 9.
- W. Magnus and S. Winkler, Hill's Equation, John Wiley and Sons, New York, 1966. MR 33:5991
- 10.
- P. Ungar, Stable Hill equations, Comm. Pure Appl. Math. 14 (1961), 707-710. MR 31:423
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
34B30, 34L15
Retrieve articles in all Journals with MSC
(1991):
34B30, 34L15
Additional Information:
Min-Jei
Huang
Affiliation:
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 30043
Email:
mjhuang@math.nthu.edu.tw
DOI:
10.1090/S0002-9939-97-03705-2
PII:
S 0002-9939(97)03705-2
Keywords:
Hill equation,
eigenvalue,
instability interval,
symmetric single well potential.
Received by editor(s):
July 10, 1995
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1997,
American Mathematical Society
|
Comments: webmaster@ams.org