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Asymptotic theory for a class of fourth-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, College of Science, University of Bahrain, P. O. Box 32038, Isa Town, State of Bahrain
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Abstract

An asymptotic theory is developed for a class of fourth-order differential equations. Under a general conditions on the coefficients of the differential equation we obtained the forms of the asymptotic solutions such that the solutions have different orders of magnitude for large x.

MSC classification

Secondary: 34E05: Asymptotic expansions
Type
Research Article
Information
Mathematika , Volume 43 , Issue 1 , June 1996 , pp. 198 - 208
Copyright
Copyright © University College London 1996

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References

1.Eastham, M. S. P.. Asymptotic formula of Liouville-Green type for higher-order differential equations. J. London Math. Soc. (2), 28 (1983), 507–518.CrossRefGoogle Scholar
2.Eastham, M. S. P.. The asymptotic solution of linear differential systems. Mathematika, 32 (1985), 131–138.Google Scholar
3.Eastham, M. S. P.. On the eigenvectors for a class of matrices arising from quasi-derivatives. Proc. Roy. Soc. Edinburgh Sect. A, 97 (1984), 73–78.Google Scholar
4.Eastham, M. S. P.. Asymptotic formulae for a critical class of fourth-order differential equations. Proc. Roy. Soc. London ser. A, 383 (1982), 465–476.Google Scholar
5.Eastham, M. S. P.. The asymptotic solution of linear differential systems. Applications of the Levinson theorem (Oxford; Clarendon Press, 1989).Google Scholar
6.Everitt, W. N. and Zettl, A.. Generalized symmetric ordinary differential expressions I, the general theory. Nieuw Arch. Wisk., 27 (1979), 363–397.Google Scholar
7.Fedorjuk, M. V.. The asymptotic behaviour of solutions of ordinary linear differential equations of order n. Soviet Math. DoKL., 6 (1965), 1528–1530.Google Scholar
8.Fedorjuk, M. V.. Asymptotic methods in the theory of one-dimensional singular differential operators. Trans. Moscow Mat. Soc, 15 (1966b), 333–386 in the Am. Math. Soc, translation.Google Scholar
9.Hinton, D. B.. Asymptotic behaviour of solutions of . J. Dig. Equations, 4 (1968), 590–596.Google Scholar
10.Levinson, N.. The asymptotic nature of solutions of linear differential equations. Duke Math. J., 15 (1948), 111–126.Google Scholar