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The asymptotic distribution of the eigenvalues of right definite multiparameter Sturm-Liouville systems

Published online by Cambridge University Press:  20 January 2009

Bryan P. Rynne
Bryan P. Rynne
Affiliation:
Department of MathematicsHeriot-Watt UniversityRiccarton Edinburgh EH14 4AS, Scotland
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Abstract

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This paper studies the asymptotic distribution of the multiparameter eigenvalues of a right definite multiparameter Sturm–Liouville eigenvalue problem. A uniform asymptotic analysis of the oscillation number of solutions of a single Sturm–Liouville type equation with potential depending on a general parameter is given; these results are then applied to the system of multiparameter Sturm–Liouville equations to give the asymptotic eigenvalue distribution for the system as a function of a “multi-index” oscillation number.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 36 , Issue 1 , February 1993 , pp. 35 - 47
Copyright
Copyright © Edinburgh Mathematical Society 1993

References

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