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Asymptotics of eigenvalues of the first boundary-value problem for singularly perturbed second-order differential equation with turning points

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Abstract

We consider a second-order linear differential equation of with a small factor at the highest derivative. We study the asymptotic behavior of eigenvalues of the first boundary-value problem (the Dirichlet problem) under the assumption that turning points (points where the coefficient at the first derivative equals to zero) exist. It has been shown that only the behavior of coefficients of the equation in a small neighborhood of the turning points is essential. The main result is a theorem on the limit values of the eigenvalues of the first boundary-value problem.

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Authors and Affiliations

  1. Demidov Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000, Russia

    S. A. Kaschenko

  2. National Research Nuclear University MEPhI, sh. Kashirskoe 31, Moscow, 115409, Russia

    S. A. Kaschenko

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  1. S. A. Kaschenko
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Correspondence to S. A. Kaschenko.

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Original Russian Text © S.A. Kaschenko, 2015, published in Modelirovanie i Analiz Informatsionnykh Sistem, 2015, Vol. 22, No. 5, pp. 682–710.

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Kaschenko, S.A. Asymptotics of eigenvalues of the first boundary-value problem for singularly perturbed second-order differential equation with turning points. Aut. Control Comp. Sci. 50, 636–656 (2016). https://doi.org/10.3103/S0146411616070105

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  • DOI: https://doi.org/10.3103/S0146411616070105

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