Global study on analytic solutions of functional equations

函数方程解析解的全局研究

• 批准号: 13640221
• 负责人: SHIMOMURA Shun
• 金额: $ 2.24万
• 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: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640221/
• 关键词: asymptotics; Painleve equations; value distribution; growth order; Garnie system; PI-hierarchy; Painleve方程式; PI-hierarchy

1. We have studied Riceati differential equations with doubly periodic coefficients. It was shown that all the periodic solutions are doubly periodic, Also we btained their periods and expressions.2. We have studied the distribution of zero of solutions satisfying linear differential equations with simply periodic meromorphic coefficients. Using Stokes phenomena of solutions, we gave estimates for zero-frequency of solutions of a class of equations containing Hill equations and Mathev equations.3. For Painleve transcendents (I), (II), (IV), we obtained estimates for the growth. For Painleve transcendents (III), (V) on the universal covering, we obtained estimates for the growth. For (I), we obtained a lower estimate as well. We studied the value distribution of small target as well.4. For higher order Painleve equations belonging to PI-hierarchy, we obtained a lower estimate for the frequency of poles of meromorphic solutions.

1.研究了具有双周期系数的Riceati微分方程.证明了所有的周期解都是双周期的，并给出了它们的周期和表达式.研究了具有单周期亚纯系数的线性微分方程解的零点分布。利用解的Stokes现象，给出了一类包含Hill方程和Mathev方程的方程解的零频率估计.对于Painleve超越（I），（II），（IV），我们得到了增长的估计.对于泛覆盖上的Painleve超越（III），（V），我们得到了增长的估计.对于（I），我们也得到了一个较低的估计。研究了小目标的价值分布.对于属于PI族的高阶Painleve方程，我们得到了亚纯解的极点频率的一个较低估计。

项目成果

Katsuya Ishizaki, Ilpo Laine, Shun Shimomura, Kazuya Tohge: "Riccati differential equations with elliptic coefficiets, II"Tohoku Math. J.. (to appear).

Katsuya Ishizaki、Ilpo Laine、Shun Shimomura、Kazuya Tohge：“带椭圆系数的 Riccati 微分方程，II”东北数学。

Shun Shimomura: "Osci llanon results for n-th order linear difteventcal eguations with meromorpbs periodic cefficients"Nagoya Math.J.. 166. 55-82 (2002)

Shun Shimomura：“具有 meromorpbs 周期系数的 n 阶线性 difteventcal 方程的振荡结果”Nagoya Math.J.. 166. 55-82 (2002)

Shun Shimomura: "On defiuencies of small functions for Painleve transcendents of the fourth kind"Ann.Acad.Sci.Fenn.Ser.AI Math.. (to appear).

Shun Shimomura：“关于第四类 Painleve 超验者的小函数的缺陷”Ann.Acad.Sci.Fenn.Ser.AI Math..（即将出现）。

Norio, Kikuchi: "Holder estimates of solutions to difference partial differential equations of elliptic-parabolic type"J.Geom.Anal. 11. 77-89 (2001)

Norio, Kikuchi：“椭圆抛物型差分偏微分方程解的持有者估计”J.Geom.Anal。

Shun Shimomura: "Lower estimates for the growth of Painleve transcendents"Funkcial.Ehvac.. to appear.

Shun Shimomura：“对 Painleve 超越者的增长的较低估计”Funkcial.Ehvac .. 出现。