Construction of asymptotics of solutions of ordinary differential equations with holomorphic coefficients in a neighborhood of infinity

2018 ◽  
Author(s):  
Mariya Viktorovna Korovina
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Asymptotics Of Solutions

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

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2249
Author(s):  
Maria Korovina
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Principal Symbol ◽  
Classical Problem ◽  
Multiple Roots ◽  
Asymptotics Of Solutions ◽  
Linear Ordinary Differential Equations ◽  
Linear Differential ◽  
Poincaré Problem ◽  
Irregular Singular Points

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.

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