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On the number of solutions of right-definite problems with a convergent Dirichlet integral

Published online by Cambridge University Press:  14 November 2011

M. S. P. Eastham
M. S. P. Eastham
Affiliation:
Chelsea College (University of London), LondonSW3 6LX
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Synopsis

A recently developed asymptotic theory of higher-order differential equations is applied to problems of right-definite type to determine the numbers M+, M− of linearly independent solutions with a convergent Dirichlet integral, M+ and M− referring to the usual upper and lower λ.-half-planes. Particular attention is given to the phenomenon noted by Karlsson in which one of M+ and M− is maximal but not the other. Conditions are given under which M+ (say) is maximal and M− is the same, one less, and two less.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 91 , Issue 3-4 , 1982 , pp. 347 - 360
Copyright
Copyright © Royal Society of Edinburgh 1982

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