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Asymptotics of Solutions of Linear Differential Equations with Holomorphic Coefficients in the Neighborhood of an Infinitely Distant Point

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  • Maria Korovina

    (Department of General Mathematics, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, GSP-1, 1-52, Leninskiye Gory, 119991 Moscow, Russia)

Abstract

This study is devoted to the description of the asymptotic expansions of solutions of linear ordinary differential equations with holomorphic coefficients in the neighborhood of an infinitely distant singular point. This is a classical problem of analytical theory of differential equations and an important particular case of the general Poincare problem on constructing the asymptotics of solutions of linear ordinary differential equations with holomorphic coefficients in the neighborhoods of irregular singular points. In this study we consider such equations for which the principal symbol of the differential operator has multiple roots. The asymptotics of a solution for the case of equations with simple roots of the principal symbol were constructed earlier.

Suggested Citation

  • Maria Korovina, 2020. "Asymptotics of Solutions of Linear Differential Equations with Holomorphic Coefficients in the Neighborhood of an Infinitely Distant Point," Mathematics, MDPI, vol. 8(12), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2249-:d:465289
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    References listed on IDEAS

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    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. Maksim V. Kukushkin, 2020. "On One Method of Studying Spectral Properties of Non-selfadjoint Operators," Abstract and Applied Analysis, Hindawi, vol. 2020, pages 1-13, September.
    3. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
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    Cited by:

    1. Maria V. Korovina & Hovik A. Matevossian, 2022. "Uniform Asymptotics of Solutions of Second-Order Differential Equations with Meromorphic Coefficients in a Neighborhood of Singular Points and Their Applications," Mathematics, MDPI, vol. 10(14), pages 1-21, July.

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