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Multiplicities of eigenvalues of a vector-valued Sturm-Liouville problem

Part of: Boundary value problems

Published online by Cambridge University Press:  26 February 2010

Qingkai Kong
Qingkai Kong
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, U.S.A. E-mail: kong@math.niu.edu
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Abstract

This paper concerns the spectrum of the r-dimensional Sturm–Liouville equation y″ + (λI − Q(x))y = 0 with the Dirichlet boundary conditions, where Q is an r × r symmetric matrix. It is proved that, under certain conditions on Q, this problem can only have a finite number of eigenvalues with multiplity r. Further discussion is given for the multiplicities of eigenvalues when Q is an r × r Jacobian matrix.

MSC classification

Secondary: 34B24: Sturm-Liouville theory
Type
Research Article
Information
Mathematika , Volume 49 , Issue 1-2 , June 2002 , pp. 119 - 127
Copyright
Copyright © University College London 2002

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References

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