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On a problem of R. G. D. Richardson

Published online by Cambridge University Press:  20 January 2009

Paul Binding  and
Hans Volkmer
Paul Binding
Affiliation:
Department of Mathematics and StatisticsUniversity of CalgaryCalgary, AlbertaCanada, T2N 1N4
Hans Volkmer
Affiliation:
Department of Mathematical SciencesUniversity of Wisconsin—MilwaukeeP.O. Box 413Milwaukee, Wisconsin 53201, U.S.A.
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Abstract

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In 1913 Richardson published necessary and sufficient conditions for a system of three Sturm–Liouville equations, linked by three parameters, to possess eigenfunctions with arbitrarily many zeros. His work contains errors, but we give conditions of his type valid for k self-adjoint equations, with k parameters.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 3 , October 1992 , pp. 337 - 348
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

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