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Open AccessArticle

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

1
Lomonosov Moscow State University, 119991 Moscow, Russia
2
Moscow Aviation Institute (National Research University), 125993 Moscow, Russia
3
Russian University of Transport (MIIT), 127994 Moscow, Russia
*
Authors to whom correspondence should be addressed.
Math. Comput. Appl. 2019, 24(1), 16; https://doi.org/10.3390/mca24010016
Received: 26 December 2018 / Revised: 24 January 2019 / Accepted: 26 January 2019 / Published: 28 January 2019
(This article belongs to the Special Issue Mathematical Modeling in Physical Sciences)
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. View Full-Text
Keywords: re-quantization method; asymptotic; holomorphic coefficient; Laplace–Borel transform re-quantization method; asymptotic; holomorphic coefficient; Laplace–Borel transform
MDPI and ACS Style

Korovina, M.; Smirnov, I.; Smirnov, V. 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. Math. Comput. Appl. 2019, 24, 16.

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