Construction of solutions of nonlinear irregular singular differential equations by Borel summable functions

被引：0

作者：

Ouchi, Sunao ^{[1
]}

机构：

[1] Sophia Univ, Tokyo, Japan

来源：

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2025年 / 77卷 / 01期

关键词：

irregular singular; Borel summable; transseries; Painleve equation; POWER-SERIES SOLUTIONS; SYSTEMS; MULTISUMMABILITY; SUMMABILITY; FORMS;

D O I：

10.2969/jmsj/90839083

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A system of nonlinear differential equations x(1+gamma)(dY/dx) = F-0(x) + A(x)Y + F(x, Y) (gamma >= 1) is considered. The origin x = 0 is irregular singular. There exist pioneering works about them. We study more precisely than preceding works, the meaning of asymptotic expansion of transformations and solutions by using Borel summable functions in asymptotic analysis and construct exponential series solutions often called transseries.

引用

页码：229 / 254

页数：26

共 23 条

[1]

Balser W., Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations, (2000)

[2]

Balser W., Braaksma B. L. J., Ramis J.-P., Sibuya Y., Multisummability of formal power series solutions of linear ordinary differential equations, Asymptotic Anal, 5, pp. 27-45, (1991)

[3]

Braaksma B. L. J., Multisummability of formal power series solutions of nonlinear meromorphic differential equations, Ann. Inst. Fourier (Grenoble), 42, pp. 517-540, (1992)

[4]

Braaksma B. L. J., Kuik R., Resurgence relations for classes of differential and difference equations, Ann. Fac. Sci. Toulouse Math, 13, 6, pp. 479-492, (2004)

[5]

Braaksma B. L. J., Stolovich L., Small divisors and large multipliers, Ann. Inst. Fourier (Grenoble), 57, pp. 603-628, (2007)

[6]

Canalis-Durand M., Mozo-Fernandes J., Schafke R., Monomial summability and doubly singular differential equations, J. Differential Equations, 233, pp. 485-511, (2007)

[7]

Costin O., On Borel summation and Stokes phenomena for rank-1 nonlinear systems of ordinary differential equations, Duke Math. J, 93, pp. 289-344, (1998)

[8]

Costin O., Topological construction of transseries and introduction to generalized Borel summability, Analyzable Functions and Applications, Contemp. Math, 373, pp. 137-175, (2005)

[9]

Costin O., Costin R. D., On the formation of singularities of solutions of nonlinear differential systems in antistokes directions, Invent. Math, 145, pp. 425-485, (2001)

[10]

Costin R. D., Truncated solutions of Painlevé equation P<sub>V</sub>, SIGMA Summetry Integrability Geom. Methods Appl, 14, (2018)

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