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