Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On a conjecture concerning the means of the eigenvalues of random Sturm-Liouville boundary value problems

Author: William E. Boyce
Journal: Quart. Appl. Math. 38 (1980), 241-245
MSC: Primary 34B25; Secondary 34F05
DOI: https://doi.org/10.1090/qam/580882
MathSciNet review: 580882
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Abstract: It has been known for several years that the expected value $ \left\langle {{\lambda _1}} \right\rangle $ of the smallest eigenvalue of a self-adjoint positive definite random Sturm-Liouville boundary value problem satisfies the relation $ \left\langle {{\lambda _1}} \right\rangle \le {\mu _1}$ where $ {\mu _1}$ is the smallest eigenvalue of the corresponding deterministic problem obtained by replacing each random coefficient by its mean. It has been an open question whether similar inequalities are valid for the higher eigenvalues. The answer is negative, as shown by the counterexample given in this note.

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DOI: https://doi.org/10.1090/qam/580882
Article copyright: © Copyright 1980 American Mathematical Society

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