Application of Resurgent Analysis to the Construction of Asymptotics of Linear Differential Equations with Degeneration in Coefficients

2021 ◽  
Author(s):  
M. V. Korovina
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Linear Differential ◽  
Resurgent Analysis

scholarly journals On a Problem Arising in Application of the Re-Quantization Method to Construct Asymptotics of Solutions to Linear Differential Equations with Holomorphic Coefficients at Infinity

2019 ◽  
Vol 24 (1) ◽  
pp. 16 ◽  
Author(s):  
Maria Korovina ◽  
Ilya Smirnov ◽  
Vladimir Smirnov
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Analytical Theory ◽  
Uniform Asymptotics ◽  
Quantization Method ◽  
Asymptotics Of Solutions ◽  
Borel Transform ◽  
Analysis Methods ◽  
Linear Differential ◽  
Resurgent Analysis

The re-quantization method—one of the resurgent analysis methods of current importance—is developed in this study. It is widely used in the analytical theory of linear differential equations. With the help of the re-quantization method, the problem of constructing the asymptotics of the inverse Laplace–Borel transform is solved for a particular type of functions with holomorphic coefficients that exponentially grow at zero. Two examples of constructing the uniform asymptotics at infinity for the second- and forth-order differential equations with the help of the re-quantization method and the result obtained in this study are considered.

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