Global study of functional equations and special functions

函数方程和特殊函数的全局研究

• 批准号: 15540212
• 负责人: SHIMOMURA Shun
• 金额: $ 1.92万
• 依托单位: Keio University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540212/
• 关键词: Painleve equations; growth order; value distribution; Painleve hierarchy; Riccati equation; doubly periodic; Pain leve超越関数; 値分布; 位数; Riccati方程式; Pain leve property

1.For Painleve transcendents of I, II, IV types, we estimated the growth order. The results are as follows : P_I=5/2 for I ; 3/2【less than or equal】P_<II>【less than or equal】3 for II ; and 2【less than or equal】P_<IV>【less than or equal】4 for IV.2.We proved the Painleve property for all Painleve equations.3.We considered solutions of the third and the fifth Painleve equations on the universal covering space, and obtained some estimates for the growth order.4.We obtained a lower estimate for the growth order of solutions of the first Painleve hierarchy, and also estimated the frequency of poles and α-points of them.5.We presented a series of systems of differential equations which is equivalent to the first Painleve hierarchy, and proved the Painleve property.6.We estimated the growth order of solutions of Riccati equations with doubly periodic coefficients.

1.对于I，II，IV类型的Painleve超然，我们估计了生长顺序。结果如下：i的p_i = 5/2； 3/2 [小于或相等] p_ <ii> [小于或相等] 3； and 2 [less than or equal] P_<IV>[less than or equal] 4 for IV.2.We provided the Painleve property for all Painleve equations.3.We considered solutions of the third and the fifth Painleve equations on the universal covering space, and obtained some estimates for the growth order.4.We obtained a lower estimate for the growth order of solutions of the first Painleve hierarchy, and also estimated the frequency of poles and α-points of它们。5。我们提出了一系列的微分方程系统，这些系统等同于第一个Painleve层次结构，并提供了Painleve的性质。6。我们估计了具有双重周期系数的Riccati方程解决方案的增长顺序。

项目成果

Shun Shimomura: "On the number of poles of the first Pain leve transcendents and higher order analogues II"数理解析研究所講究録. 13 16. 13-18 (2003)

下村俊：“关于第一级超越级和高阶类似物的极数 II”数学科学研究所 Kokyuroku. 13 16. 13-18 (2003)

Meromorphic solutions of Riccati differential equations with doubly periodic coefficients

具有双周期系数的Riccati微分方程的亚纯解

• 期刊: J.Math.Anal.Appl. (to appear)
• 作者: G.Chen;H.Enomoto 他;K.Ota;S.Shimomura;S.Shimomura
• 通讯作者: S.Shimomura

Shun Shimomura: "Nevanlinna理論の微分方程式への応用"神戸大学理学部数学教室. 89 (2003)

Shun Shimomura：“Nevanlinna 理论在微分方程中的应用”神户大学理学院数学系 89（2003）。

Growth of modified Painleve transcendents of the fifth and the third kind

第五类和第三类改进的Painleve超越者的生长

• 发表时间: 2004
• 期刊: Forum Math. 16
• 作者: Shun Shimomura;Shun Shimomura;Shun Shimomura
• 通讯作者: Shun Shimomura

Shun Shimomura: "Growth of the first, the second and the fourth Pain leve transcendents"Math.Proc.Camb.Phil.Soc.. 134. 259-269 (2003)

Shun Shimomura：“第一、第二和第四疼痛级别超越者的成长”Math.Proc.Camb.Phil.Soc.. 134. 259-269 (2003)