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The existence of eigenvalues embedded in the continuous spectrum of ordinary differential operators†

Published online by Cambridge University Press:  14 February 2012

M. S. P. Eastham  and
J. B. McLeod
M. S. P. Eastham
Affiliation:
Chelsea College, University of London
J. B. McLeod
Affiliation:
Wadham College, Oxford
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Synopsis

In answer to two questions raised by W. N. Everitt, we show that, given p > l and any countably infinite set of isolated points on the positive λ-axis, there is a q(x) in Lp(0, ∞) for which the set of points constitutes the point-continuous spectrum associated with the equation y”(x) + {λ − q(x)}y(x) = 0 (0≦x<∞) and some homogeneous boundary condition at x = 0.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 79 , Issue 1-2 , 1977 , pp. 25 - 34
Copyright
Copyright © Royal Society of Edinburgh 1977

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