Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Upper bounds for the means of eigenvalues of random boundary value problems with weakly correlated coefficients

Authors: William E. Boyce and Ning Mao Xia
Journal: Quart. Appl. Math. 42 (1985), 439-454
MSC: Primary 34F05; Secondary 34B05
DOI: https://doi.org/10.1090/qam/766881
MathSciNet review: 766881
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Abstract: This paper concerns eigenvalue problems for second-order random differential equations with weakly correlated coefficients. The random problem and the mean (deterministic) problem are embedded in a parametrized problem whose eigenvalues are expanded in a power series in the parameter. This expansion leads, via the variational characterization of the eigenvalues, to computationally accessible upper bounds for the mean values of the eigenvalues of the original problem.

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  • [1] W. E. Boyce, Random eigenvalue problems, in Probabilistic Methods in Applied Mathematics, vol. 1, A. T. Bharucha-Reid (editor), Academic Press, New York, 1968, 1-73 MR 0263171
  • [2] W. E. Boyce, On a conjecture concerning the means of the eigenvalues of random Sturm-Liouville boundary value problems, Q. Appl. Math., 38, 241-245 (1980) MR 580882
  • [3] W. E. Boyce and Ning-Mao Xia, The approach to normality of the solutions of random boundary and eigenvalue problems with weakly correlated coefficients, Q. Appl. Math., 40, 419-445 (1983) MR 693876
  • [4] L. Collatz, Eigenwertprobleme und ihre numerische Behandlung, Chelsea Publishing Co., New York, 1948
  • [5] L. Collatz, Eigenwertaufgaben mit technischen Anwendungen, Geest and Portig, Leipzig, 1963 MR 0152101
  • [6] R. Courant and D. Hilbert, Methods of mathematical physics, vol. 1, Interscience, New York, 1953 MR 0065391
  • [7] W. Purkert and J. vom Scheidt, Zur approximativen Lösung des Mittelungsproblems für die Eigenwerte stochastischer Differentialoperatoren, ZAMM, 57, 515-525 (1977) MR 480129
  • [8] W. Purkert and J. vom Scheidt, Eine Störungsrechnung für die Eigenwerte und Eigenvektoren zufälliger Matrizen, Beiträge Zur Analysis, 11 (1978), 113-135
  • [9] W. Purkert and J. vom Scheidt, Ein Grenzverteilungssatz für stochastische Eigenwertprobleme, ZAMM, 59 (1979), 611-623 MR 563447
  • [10] W. Purkert and J. vom Scheidt, Stochastic eigenvalue problems for differential equations, Rep. Math. Phys., 15 (1979), 205-227 MR 554155
  • [11] J. vom Scheidt and W. Purkert, Limit theorems for solutions of stochastic differential equation problems, Int. J. Math. and Math. Sci., 3 (1980), 113-149 MR 576633

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DOI: https://doi.org/10.1090/qam/766881
Article copyright: © Copyright 1985 American Mathematical Society

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