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13.—On a Problem of Transformations between Limit-circle and Limit-point Differential Equations

Published online by Cambridge University Press:  14 February 2012

F. Neuman
F. Neuman
Affiliation:
Brno, Czechoslovakia.
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Extract

1. In this article the following problem proposed by W. N. Everitt is considered: ‘Under what conditions is it possible to transform a differential equation

which is limit-circle at b1 into an equation of the form

which is limit-point at b2?'

A differential equation of the above type on [a, b) is said to be limit-circle at b iff b is a singular point and every solution . If b is singular and there exists a , then the equation is said to be limit-point at b. See [3] or [4] page 501, also for further details.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 72 , Issue 3 , 1975 , pp. 187 - 193
Copyright
Copyright © Royal Society of Edinburgh 1975

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References

References To Literature

[1]Barrett, J. H., 1969. Oscillation theory of ordinary linear differential equations. Adv. Math., 3, 415–509.CrossRefGoogle Scholar
[2]Boruvka, O., 1967. Lineare Differentialtransformationen, 2. Ordnung. Berlin: VEB. (English edn. Linear Differential Transformations of the Second Order. London: E.U.P., 1971).Google Scholar
[3]Everitt, W. N., 1972. On the limit-circle classification of second-order differential expressions. Q.Jl Math., 23, 193–196.CrossRefGoogle Scholar
[4]Hille, E., 1969. Lectures on Ordinary Differential Equations. Reading, Mass: Addison-Wesley.Google Scholar
[5]Neuman, F., 1971. L2-solutions of y″ = q(t)y and a functional equation. Aequationes Math., 6, 162–169.CrossRefGoogle Scholar