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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

1.Agranovich, Z. S. and Marchenko, V. A.. The Inverse Problem of Scattering Theory. Gordon and Breach, New York, 1993.Google Scholar
2.Atkinson, F. V.. Discrete and Continuous Boundary Problems. Academic Press, New York, 1964.Google Scholar
3.Shen, C.-L. and Shieh, C.-T.. On the multiplicity of eigenvalues of a vectorial Sturm-Liouville differential equations and some related spectral problems. Proc. Amer. Math. Soc., 127 (1999), 2943–2952.CrossRefGoogle Scholar
4.Weidmann, J.. Spectral Theory of Ordinary Differential Operators. Lecture Notes in Math., 1285, Springer-Verlag. Berlin, Heidelberg, 1987.CrossRefGoogle Scholar