ON GEVREY ORDERS OF FORMAL POWER SERIES SOLUTIONS TO THE THIRD AND FIFTH PAINLEV EQUATIONS NEAR INFINITY

被引：2

作者：

Parusnikova, Anastasia V. ^{[1
]}

机构：

[1] Natl Res Univ Higher Sch Econ, Bolshoi Trekhsvjatitelskii Per 3, Moscow 109028, Russia

来源：

OPUSCULA MATHEMATICA | 2014年 / 34卷 / 03期

关键词：

Painleve equations; Newton polygon; asymptotic expansions; Gevrey orders;

D O I：

10.7494/OpMath.2014.34.3.591

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The question under consideration is Gevrey summability of formal power series solutions to the third and fifth Painleve equations near infinity. We consider the fifth Painleve equation in two cases: when alpha beta gamma delta not equal 0 and when alpha beta gamma not equal 0; delta = 0 and the third Painleve equation when all the parameters of the equation are not equal to zero. In the paper we prove Gevrey summability of the formal solutions to the fifth Painleve equation and to the third Painleve equation, respectively.

引用

页码：591 / 599

页数：9

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