Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-26T16:11:52.340Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic theory for third-order differential equations

Part of: Asymptotic theory

Published online by Cambridge University Press:  26 February 2010

A. S. A. Al-Hammadi
A. S. A. Al-Hammadi
Affiliation:
Department of Mathematics, University of Bahrain, P.O. Box 32038, Manama, Bahrain.
Get access

Extract

We examine the asymptotic form of a fundamental set of solutions of the third-order equation

as x → ∞, where the leading coefficient q is nowhere zero in some interval [a, ∞). The equation is self-adjoint in the case when p, r and iq are real. However, our analysis is not confined to this case, and we generally take the coefficients to be complex-valued.

MSC classification

Secondary: 34E99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 35 , Issue 2 , December 1988 , pp. 225 - 232
Copyright
Copyright © University College London 1988

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

1.Al-Hammadi, A. S. A.. Asymptotic theory for third-order differential equations. Ph.D. thesis (University of London, 1986).Google Scholar
2.Eastham, M. S. P.. Asymptotic formulae of Liouville-Green type for higher-order differential equations. J. London Math. Soc. (2), 28 (1983), 507–518.CrossRefGoogle Scholar
3.Eastham, M. S. P.. On the eigenvectors for a class of matrices arising from quasi-derivatives. Proc. Roy. Soc. Edinburgh, 97A (1984), 73–78.CrossRefGoogle Scholar
4.Eastham, M. S. P.. The asymptotic solution of linear differential systems. Mathematika, 32 (1985), 131–138.CrossRefGoogle Scholar
5.Eastham, M. S. P.. A repeated transformation in the asymptotic solution of linear differential systems. Proc. Roy. Soc. Edinburgh, 102A (1986), 173–188.CrossRefGoogle Scholar
6.Everitt, W. N. and Zettl, A.. Generalized symmetric ordinary differential expressions I: the general theory. Nieuw Arch. Wist., 27 (1979), 363–397.Google Scholar
7.Grudniewicz, C. G. M.. Asymptotic methods for fourth-order differential equations. Proc Roy. Soc. Edinburgh, 87A (1980), 53–63.CrossRefGoogle Scholar
8.Levinson, N.. The asymptotic nature of solutions of linear differential equations. Duke Math. J., 15 (1948), 111–126.CrossRefGoogle Scholar
9.Pfeiffer, G. W.. Asymptotic Solutions of y‴ + q′+ ry = 0. J. of Differential Equations, 11 (1972), 145–155.CrossRefGoogle Scholar
10.Unsworth, K.. Asymptotic expansions and deficiency indices associated with third-order self-adjoint differential operators. Quart. J. Math. Oxford, 24 (1973), 177–188.CrossRefGoogle Scholar