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20.—On the Limit-point and Limit-circle Theory of Second-order Differential Equations

Published online by Cambridge University Press:  14 February 2012

K. S. Ong
K. S. Ong
Affiliation:
Department of Mathematics, University of Toronto.
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Synopsis

In this paper the Weyl limit-point and limit-circle theory of second-order differential equations is extended to the case that the weight function is allowed to take on both positive and negative values—the polar case. This extension is achieved using Weyl's limit circle method.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 72 , Issue 3 , 1975 , pp. 245 - 256
Copyright
Copyright © Royal Society of Edinburgh 1975

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References

References to Literature

[1]Atkinson, F. V.Everitt, W. N. and Ong, K. S. On the m-coefficient of Weyl for a differential equation with an indefinite weight function. Proc. Lond. Math. Soc. (To appear.)Google Scholar
[2]Atkinson, F. V., Everitt, W. N. and Ong, K. S.. Some remarks on the zeros of the m-coefficient of Weyl. (To appear.)Google Scholar
[3]Coddington, E. A. and Levinson, N., 1955. Theory of Ordinary Differential Equations. New York: McGraw-Hill.Google Scholar
[4]Everitt, W. N., 1962. Self-adjoint boundary value problems on finite intervals. J. Lond. Math. Soc., 37, 372–384.CrossRefGoogle Scholar
[5]Everitt, W. N.,, 1963. A note on the self-adjoint domains of second-order differential equations. Quart. Jl Math., 14, 41–45.CrossRefGoogle Scholar
[6]Hellwig, G., 1967. Differential Operators of Mathematical Physics. New York: Addison-Wesley.Google Scholar
[7]Ong, K. S. The limit-circle and limit-point criterion for second-order differential equations with an indefinite weight function. (To appear.)Google Scholar
[7]Ong, K. S. The limit-circle and limit-point criterion for second-order differential equations with an indefinite weight function. (To appear.)Google Scholar
[8]Pleijel, A., 1969. Some remarks about the limit point and limit circle theory. Ark. Mat., 7, 543–550.CrossRefGoogle Scholar
[9]Pleijel, A.,, 1971. Complementary remarks about the limit point and limit circle teory. Ark. Mat., 8, 45–47.CrossRefGoogle Scholar
[10]Titchmarsh, E. C., 1962. Eigenfunction Expansions associated with Second-order Differential Equation, I. O.U.P.CrossRefGoogle Scholar
[11]Weyl, H., 1910. Über gewöhnliche Differentialgleichungen mit Singularitäten und die Zugehörigen Entwicklungen Willkurlicher Funktiononen. Math. Annln, 68, 220–269.CrossRefGoogle Scholar
[12]Yosida, K., 1960. Lectures on Differential and Integral Equations. New York: Interscience.Google Scholar