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Estimates of eigenvalues of self-adjoint boundary-value problems with periodic coefficients

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Abstract

We consider self-adjoint boundary-value problems with discrete spectrum and coefficients periodic in a certain coordinate. We establish upper bounds for eigenvalues in terms of the eigenvalues of the corresponding problem with averaged coefficients. We illustrate the results obtained in the case of the Hill vector equation and for circular and rectangular plates with periodic coefficients.

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Authors and Affiliations

  1. Institute of Transport Systems and Technologies, Ukrainian Academy of Sciences, Dnepropetrovsk

    A. A. Zevin

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  1. A. A. Zevin
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 5, pp. 632–638, May, 1998.

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Zevin, A.A. Estimates of eigenvalues of self-adjoint boundary-value problems with periodic coefficients. Ukr Math J 50, 719–725 (1998). https://doi.org/10.1007/BF02514325

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  • DOI: https://doi.org/10.1007/BF02514325

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