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16.—Square Integrable Solutions of Perturbed Linear Differential Equations*

Published online by Cambridge University Press:  14 February 2012

James S. W. Wong
James S. W. Wong
Affiliation:
Department of Mathematics, University of Iowa, U.S.A.
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Synopsis

This paper is concerned with solutions of the ordinary differential equation

where ℒ is a real formally self-adjoint, linear differential expression of order 2n, and the perturbed term f satisfies

for some σ∈[0, 1]. Here λ(·) is locally integrable on [0,∞).

In particular it is shown, under circumstances detailed in the text, that (*) possesses solutions in the Hilbert function space L2(0,∞).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 73 , 1975 , pp. 251 - 254
Copyright
Copyright © Royal Society of Edinburgh 1975

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