Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Lower bounds for eigenvalues of Sturm-Liouville problems with discontinuous coefficients: integral equation methods


Authors: C. O. Horgan, J. P. Spence and A. N. Andry
Journal: Quart. Appl. Math. 39 (1982), 455-465
MSC: Primary 34B25
DOI: https://doi.org/10.1090/qam/644100
MathSciNet review: 644100
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Abstract: This paper is concerned with application of the theory of Fredholm integral equations to Sturm-Liouville problems with discontinuous coefficients. Such problems occur naturally in many areas of application involving mechanics of heterogeneous media. Due to the nonsmoothness of the coefficients, the eigenvalue spectrum may exhibit severe irregularities. Lower bounds for eigenvalues are obtained which reflect this behavior. Numerical results are presented for example problems previously treated using other methods.


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DOI: https://doi.org/10.1090/qam/644100
Article copyright: © Copyright 1982 American Mathematical Society

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