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Non-existence of large eigenvalues of a third order differential equation

Part of: Boundary value problems

Published online by Cambridge University Press:  26 February 2010

A. M. J. Davis
A. M. J. Davis
Affiliation:
Department of Mathematics, University College London.
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Summary

The study of plasma instabilities has led to the question whether a certain third order linear differential equation involving a parameter p has solutions which vanish as x → ± ∞. Assuming existence, it is first easily shown that Rep must be positive and then, after a Fourier transform has changed the equation to one of second order, standard comparison equation techniques are used to obtain a contradiction, valid for large enough p.

MSC classification

Secondary: 34B10: Nonlocal and multipoint boundary value problems
Type
Research Article
Information
Mathematika , Volume 25 , Issue 1 , June 1978 , pp. 151 - 159
Copyright
Copyright © University College London 1978

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References

Gibson, R. D. and Kent., A. 1971, Q. Jl. Mech. Appl. Math., 24, 63–79.CrossRefGoogle Scholar
Hsieh, P-F. and Sibuya., Y. 1966, J. Math. Anal., 16, 84–103.CrossRefGoogle Scholar
Lakin, W. D.. 1972, Stud. Appl. Math., 51, 261–275CrossRefGoogle Scholar
Langer, R. E.. 1955, Trans. Amer. Math. Soc, 80, 93–123CrossRefGoogle Scholar
Lynn, R. and Keller, J. B.. 1970, Comm. Pure Appl. Math., 23, 379–408CrossRefGoogle Scholar
McKelvey, R. W.. 1955, Trans. Amer. Math. Soc, 79, 103–123CrossRefGoogle Scholar
Olver, F. W. J.. 1974, Asymptotics and Special Functions (Academic Press).Google Scholar
Olver, F. W. J.. 1977, SIAM J. Math. Anal, 8, 127–154 and 673–700CrossRefGoogle Scholar
Sibuya., Y. 1967, Acta Math., 119, 235–271CrossRefGoogle Scholar
Streifer., W. 1968, J. Math. Anal., 21, 123–125CrossRefGoogle Scholar
Whittaker, E. T. and Watson, G. N.. 1965, Modern Analysis, 4th ed. (Cambridge University Press).Google Scholar
Zwaan, A.. 1929, Arch Neerlandaises Sci. Exactes Natur Ser. 3A, 12, 1–76Google Scholar