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A directed set of Sturm–Liouville operators

Published online by Cambridge University Press:  14 November 2011

Harold E. Benzinger
Harold E. Benzinger
Affiliation:
Department of Mathematics, University of Illinois, Urbana, Illinois 61801, U.S.A
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Synopsis

Asymptotic estimates for the eigenvalues and eigenfunctions of a directed set of Sturm–Liouville operators are obtained. Particular attention is paid to the influence of the diffusion coefficient, as it becomes arbitrarily large.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 90 , Issue 1-2 , 1981 , pp. 125 - 145
Copyright
Copyright © Royal Society of Edinburgh 1981

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References

1Benzinger, H. E.. Eigenvalues of regular differential operators. Proc. Roy. Soc. Edinburgh Sect. A 79 (1977), 299–305.CrossRefGoogle Scholar
2Benzinger, H. E.. Perturbation of the heat equation. J. Differential Equations 32 (1979), 398–419.CrossRefGoogle Scholar
3Birkhoff, G. D.. Boundary value and expansion problems of ordinary linear differential equations. Trans. Amer. Math. Soc. 9 (1908), 373–395.CrossRefGoogle Scholar
4Horgan, C. O. and Nemat-Nasser, S.. Bounds on eigenvalues of Sturm–Liouville problems with discontinuous coefficients. Z. Angew. Math. Phys. 30 (1979), 77–86.CrossRefGoogle Scholar
5Ince, E. L.. Ordinary Differential Equations (New York: Dover, 1956).Google Scholar
6McNabb, A., Anderson, R. S. and Lapwood, E. R.. Asymptotic behavior of the eigenvalues of a Sturm–Liouville system with discontinuous coefficients. J. Math. Anal. Appl. 54 (1976), 741–751.CrossRefGoogle Scholar
7Neumark, M. A.. Lineare Differentialoperatoren (Berlin: Akademie-Verlag, 1960).CrossRefGoogle Scholar