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Asymptotic solution of one-dimensional spectral boundary-value problems with rapidly varying coefficients: The case of multiple spectra

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Abstract

We suggest a method for the construction of complete asymptotic expansions for eigenvalues and eigen-functions of spectral boundary-value problems for differential equations with rapidly varying coefficients in the case of multiple spectra of the averaged problem. The effect of splitting of multiple eigen-values is illustrated by an example of a special fourth-order problem.

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Authors and Affiliations

  1. Shevchenko National University, Kiev

    O. Yu. Teplinskii

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  1. O. Yu. Teplinskii
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 10, pp. 1399–1408, October, 1998.

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Teplinskii, O.Y. Asymptotic solution of one-dimensional spectral boundary-value problems with rapidly varying coefficients: The case of multiple spectra. Ukr Math J 50, 1599–1610 (1998). https://doi.org/10.1007/BF02513491

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  • DOI: https://doi.org/10.1007/BF02513491

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