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Uniform Asymptotics of Solutions of Second-Order Differential Equations with Meromorphic Coefficients in a Neighborhood of Singular Points and Their Applications

Author

Listed:
  • Maria V. Korovina

    (Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow 119991, Russia)

  • Hovik A. Matevossian

    (Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Moscow 119333, Russia
    Institute No. 3, Moscow Aviation Institute (National Research University, “MAI”), Moscow 125993, Russia)

Abstract

In this paper, we consider the problem of obtaining the asymptotics of solutions of differential operators in a neighborhood of an irregular singular point. More precisely, we construct uniform asymptotics for solutions of linear differential equations with second-order meromorphic coefficients in a neighborhood of a singular point and apply the results obtained to the equations of mathematical physics. The main results related to the construction of uniform asymptotics are obtained using resurgent analysis methods applied to differential equations with irregular singularities. These results allow us to construct asymptotics for any second-order equations with meromorphic coefficients—that is, with an arbitrary order of degeneracy. This also allows one to determine the type of a singular point and highlight the cases where the point is non-singular or regular.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2465-:d:863608
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    References listed on IDEAS

    as
    1. Hovik A. Matevossian, 2020. "Asymptotics and Uniqueness of Solutions of the Elasticity System with the Mixed Dirichlet–Robin Boundary Conditions," Mathematics, MDPI, vol. 8(12), pages 1-32, December.
    2. 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.
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