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The limit-point, limit-circle nature of rapidly oscillating potentials

Published online by Cambridge University Press:  14 February 2012

F. V. Atkinson ,
M. S. P. Eastham  and
J. B. McLeod
F. V. Atkinson
Affiliation:
Department of Mathematics, University of Toronto
M. S. P. Eastham
Affiliation:
Department of Mathematics, Chelsea College, University of London
J. B. McLeod
Affiliation:
Wadham College, University of Oxford
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Synopsis

The Weyl limit-point, limit-circle nature of the equation y″(x)–q(x)y(x) = 0(0≦ x< ∞) is analysed When q(x) has the form q(x) = xαp(xβ), where α and β are positive constants and p(t) is a continuous periodic function of t.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 76 , Issue 3 , 1977 , pp. 183 - 196
Copyright
Copyright © Royal Society of Edinburgh 1977

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