Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-19T00:42:05.329Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalised Liouville-Green asymptotic approximations for second-order differential equations

Published online by Cambridge University Press:  14 November 2011

J. S. Cassell
J. S. Cassell
Affiliation:
Department of Computing, Management Science, Mathematics and Statistics, City of London Polytechnic, 100 Minories, Tower Hill, London EC3N 1JY, U.K.
Get access Rights & Permissions [Opens in a new window]

Synopsis

The equation {r(x)y'}' = q(x)y is considered with the coefficients q and rtaking complex values. Conditions are obtained for there to be solutions with the asymptotic form , . These involve the coefficients and their derivatives up to some order N.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 103 , Issue 3-4 , 1986 , pp. 229 - 239
Copyright
Copyright © Royal Society of Edinburgh 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Atkinson, F. V., Eastham, M. S. P. and McLeod, J. B.. The limit-point, limit-circle nature of rapidly oscillating potentials. Proc. Roy. Soc. Edinburgh Sect. A 76 (1977), p183–196.CrossRefGoogle Scholar
2Cassell, J. S.. An extension of the Liouville-Green asymptotic formula for oscillatory second-order differential equations. Proc. Roy. Soc. Edinburgh Sect. A 100 (1985), 181–190.CrossRefGoogle Scholar
3Coddington, E. A. and Levinson, N.. Theory of ordinary differential equations (New York: McGraw-Hill, 1955).Google Scholar
4Eastham, M. S. P.. The Liouville-Green asymptotic theory for second-order differential equations: a new approach and some extensions. Ordinary differential equations and operators. Lecture Notes in Mathematics 1032 (Berlin: Springer, 1983).Google Scholar