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Asymptotic Formulae for the Eigenvalues of a Two Parameter System of Ordinary Differential Equations of the Second Order

Published online by Cambridge University Press:  20 November 2018

M. Faierman
M. Faierman*
Affiliation:
Loyola College, Montreal, Quebec
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The origin and importance of multiparameter Sturm-Liouville problems in mathematical physics has recently been discussed by Atkinson [1, sects. 3 and 4], [2, introduction]. In spite of the importance of such problems, and in spite of the work done in this field by such early investigators as Klein and Hilbert, Atkinson points out that in recent years this field has been relatively neglected in contrast to the single parameter case. As an example, he states that as opposed to the one parameter case, the detailed behaviour of the eigenvalues and eigenfunctions in the multiparameter Sturm-Liouville case is still far from clear.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 5 , February 1975 , pp. 657 - 665
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Atkinson, F. V., Multiparameter spectral theory, Bull. Amer. Math. Soc. 74 (1968), 1–27.Google Scholar
2. Atkinson, F. V., Multiparameter Eigenvalue Problems, Vol. 1, Academic, New York, N.Y., 1972.Google Scholar
3. Atkinson, F. V., Discrete and Continuous Boundary Problems, Academic, New York, N.Y., 1964.Google Scholar
4. Faierman, M., Asymptotic formulae for the eigenvalues of a two-parameter ordinary differential equation of the second order, Trans. Amer. Math. Soc. 168 (1972), 1–52.Google Scholar
5. Faierman, M., Boundary value problems in differential equations, Ph.D. Dissertation, University of Toronto, June, 1966.Google Scholar
6. Horn, J., Ueber eine lineare differentialgleichung zweiter ordnung mit einem willkurlichen parameter, Math. Ann. 52 (1899), 271–292.Google Scholar
7. Ince, E. L., Ordinary Differential Equations, Dover, New York, N.Y., 1956.Google Scholar
8. Richardson, R. G. D., Theorems of oscillation for two linear differential equations of the second order, Trans. Amer. Math. Soc. 13 (1912), 22–34.Google Scholar
9. Richardson, R. G. D., Über die notwendig und hinreichenden bedingungen fur das bestehen eines Kleinschen oszillationstheorems, Math. Ann. 73 (1912–13), 289–304.Google Scholar