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Bounds for the point spectrum for a Sturm-Liouville equation*

Published online by Cambridge University Press:  14 November 2011

F. V. Atkinson  and
W. N. Everitt
F. V. Atkinson
Affiliation:
Department of Mathematics, University of Toronto
W. N. Everitt
Affiliation:
Department of Mathematics, University of Dundee
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Synopsis

This paper obtains, under certain general conditions on the coefficient q, a best-possible upper bound on the real parameter λ for the differential equation

to have a non-trivial solution in the integrable-square space L2 (a, ∞).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 80 , Issue 1-2 , 1978 , pp. 57 - 66
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

1Atkinson, F. V.The asymptotic solution of second-order differential equations. Ann. Mat. Pura Appl 37 (1954), 347–378.CrossRefGoogle Scholar
2Atkinson, F. V. Asymptotic integration and the L 2-classification of second-order differential operators. Quaestiones Math., to appear.Google Scholar
3Coppel, W. A.Stability and asymptotic behaviour of differential equations (Boston: Heath, 1965).Google Scholar
4Eastham, M. S. P. On the absence of square-integrable solutions of the Sturm-Liouville equation. Lecture Notes in Mathematics 564 (Berlin: Springer, 1976).Google Scholar
5Everitt, W. N.On the spectrum of a second-order linear differential equation with a p-integrable coefficient. Applicable Anal. 2 (1972), 143–160.CrossRefGoogle Scholar
6Harris, W. A. Jr, and Lutz, D. A.Asymptotic integration of the adiabatic oscillator. J. Math. Anal. Appl. 51 (1975), 76–93.CrossRefGoogle Scholar