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

Maria Korovina
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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

Mathematics, 2020, vol. 8, issue 12, 1-15

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.

Keywords: differential equations with holomorphic coefficients; irregular singular points; Laplace–Borel transform; resurgent analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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