Instability intervals of the Ince and Hill equations

Analysis (Germany)

Volumn 25, Issue 38412, 2005, Pages 189-204

  Volkmer, Hans ^a  

^a UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846294645     PISSN: 01744747     EISSN: 21966753     Source Type: Journal    
DOI: 10.1524/anly.2005.25.3.189     Document Type: Article

References (12)

1. V.I. Arnold. Remarks on the perturbation theory for problems of Mathieu type. Russ. Math. Surv., 38:215–233,1983.
2. F.M. Arscott. Periodic Differential Equations. Macmillan, New York, 1964.
3. J. Avron and B. Simon. The asymptotics of the gap in the Mathieu equation. Ann. Phys, 134:76–84,1981.
4. P. Djakov and B. Mityagin. Smoothness of Schroedinger operator in the case of Gevrey type asymptotics of the gaps. J. Funct. Anal., 195:89–128,2002.
5. P. Djakov and B. Mityagin. Asymptotics of instability zones of the Hill operator with a two term potential. Ohio State Math. Res. Inst. Preprint 04–10, July 19, 2004 (see www.math.ohio-state.edu/mri/preprints/).
6. M. S. P. Eastham. The Spectral Theory of Periodic Differential Equations. Scottish Academic Press, Edinburgh London, 1973.
7. A. Erdelyi, W. Magnus, F. Oberhettinger, and F. Tricomi. Higher Transcendental Functions, Vol. 3. McGraw-Hill, New York, 1955.
8. H. Hochstadt. Instability intervals of Hill's equation. Commun. Pure Appl. Math., 17:251–255,1964.
9. T. Kato. Perturbation Theory for Linear Operators. Springer, Berlin Heidelberg New York, 1980.
10. D. Levy and J. Keller. Instability intervals of Hill's equation. Commun. Pure Appl. Math., 16:469–476,1963.
11. W. Magnus and S. Winkler. Hill's Equation. John Wiley & Sons, New York, 1966.
12. H. Volkmer. Coexistence of periodic solutions of Ince's equation. Analysis, 23:97–105, 2003.