Regularized asymptotics of solutions of systems of Fredholm integro-differential equations with rapidly varying kernels

2009 ◽  
Vol 45 (2) ◽  
pp. 226-239 ◽  
Author(s):  
A. A. Bobodzhanov ◽  
V. F. Safonov
Keyword(s):  
Differential Equations ◽  
Asymptotics Of Solutions ◽  
Regularized Asymptotics

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.

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.

On Asymptotics of Solutions to Some Linear Differential Equations

2019 ◽  
Vol 241 (5) ◽  
pp. 614-621
Author(s):  
K. A. Mirzoev ◽  
N. N. Konechnaya ◽  
T. A. Safonova ◽  
R. N. Tagirova
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Asymptotics Of Solutions ◽  
Linear Differential
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