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Non-standard oscillation theory for multiparameter eigenvalue problems

Published online by Cambridge University Press:  10 August 2012

P. A. Binding  and
H. Volkmer
P. A. Binding
Affiliation:
Department of Mathematics and Statistics, University of Calgary, University Drive NW, Calgary, Alberta T2N 1N4, Canada (binding@ucalgary.ca)
H. Volkmer
Affiliation:
Department of Mathematical Sciences, University of Wisconsin–Milwaukee, PO Box 413, Milwaukee, WI 53201, USA (volkmer@uwm.edu)
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Abstract

An eigenvalue problem for k Sturm–Liouville equations coupled by k parameters λ1,…,λk is considered. In contrast to the standard case, for each r, the second-order derivative in the rth equation is multiplied by λr. This problem presents various interesting features. For example, the existence of eigenvalues with oscillation counts beyond a certain (computable) value is obtained without any of the restrictive definiteness conditions known from the standard case. Uniqueness is also analysed, and the results are given greater precision via eigencurve methods in the case of two equations coupled by two parameters.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 4 , August 2012 , pp. 673 - 690
Copyright
Copyright © Royal Society of Edinburgh 2012

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