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arXiv · 2211.04650

Construction of solutions of nonlinear irregular singular differential equations by Borel summable functions and an application to Painlevé equations

Sunao Ouchi
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Abstract

A system of nonlinear differential equations $x^{1+γ}\frac{dY}{dx}= F_0(x)+A(x)Y+F(x,Y)$ is considered. We study more precisely the meaning of asymptotic expansion of transformations and solutions than preceding pioneering works, by using the theory of Borel summable functions in asymptotic analysis, and apply results to Painlevé equations.

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Sunao Ouchi. 2023-01-24. Construction of solutions of nonlinear irregular singular differential equations by Borel summable functions and an application to Painlevé equations. https://arxiv.org/abs/2211.04650

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