Hostname: page-component-74656f9884-j7cmm Total loading time: 0 Render date: 2026-11-09T21:59:31.741Z Has data issue: false hasContentIssue false
  • English
  • Français

The parameter dependent Sturm-Liouville eigenproblem with an interior simple or double pole

Published online by Cambridge University Press:  17 February 2009

Thomas M. Acho  and
Dominic P. Clemence
Thomas M. Acho
Affiliation:
Department of Mathematics, Vista University, PO Box 380, Bloemfontein 9300, Republic of South Africa; e-mail: acho-tm@blenny.vista.ac.za.
Dominic P. Clemence
Affiliation:
Department of Mathematics, North Carolina Agricultural and Technical State University, Greensboro, NC 27411, USA; e-mail: clemence@ncat.edu.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Boundary value problems where resonance phenomena are studied are most often transformable to parameter dependent Sturm-Liouville (SL) eigenproblems with interior singularities. The parameter dependent Sturm-Liouville eigenproblem with interior poles is examined. Asymptotic approximations to the solutions are obtained using an extended Langer's method to take care of the resulting complex eigenvalues and eigenfunctions.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 43 , Issue 4 , April 2002 , pp. 479 - 491
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Abramowitz, M. and Stegun, I., Handbook of mathematical functions (Dover, New York, 1965).Google Scholar
[2]Acho, T. M. and Clemence, D. P., “Sturm-Liouville eigenproblems with an interior double pole”, ZAMP 46 (1995) 459–474.Google Scholar
[3]Anyanwu, D. U., “Uniform asymptotic solutions of second order linear ordinary differential equations with singular points I. Formal theory”, J. Math. Anal. Appl. 134 (1989) 329–354.CrossRefGoogle Scholar
[4]Anyanwu, D. U., “Uniform asymptotic solutions of second order linear ordinary differential equations with singular points II. Some expansions”, J. Math. Anal. Appl. 134 (1989) 355–378.CrossRefGoogle Scholar
[5]Anyanwu, D. U. and Keller, J. B., “Asymptotic solutions of eigenvalue problems for second order ordinary differential equations”, Comm. Pure Appl. Math. 28 (1975) 753–763.CrossRefGoogle Scholar
[6]Boyd, J. P., “Sturm-Liouville eigenproblems with an interior pole”, J. Math. Phys. 22 (1981) 1575–1590.CrossRefGoogle Scholar
[7]Everitt, W. N., Gunson, J. and Zettl, A., “Some comments on Sturm-Liouville eigenvalue problems with interior singularities”, ZAMP 38 (1987) 813–838.Google Scholar
[8]Lynn, R. V. S. and Keller, J. B., “Uniform asymptotic solutions of second order linear ordinary differential equations with turning points”, Comm. Pure Appl. Math. 23 (1970) 379–489.CrossRefGoogle Scholar
[9]Shubov, M. A., “High-energy asymptotics of resonances for three-dimensional Schröodinger operator with screened Coulomb potential”, J. Math. Phys. 35 (1994) 656–679.CrossRefGoogle Scholar
[10]Simmons, A. J., “Planetary-scale disturbances in the polar winter stratosphere”, Quart. J. R. Met. Soc. 100 (1974) 76–108.Google Scholar
[11]Slater, L. J., Confluent hypergeometric functions (Cambridge University Press, 1960).Google Scholar