非线性复微分方程研究的新进展（英文）  

The New Developments in the Research of Nonlinear Complex Differential Equations

作　　者：廖良文[1] 

机构地区：[1]南京大学数学系,江苏南京210093

出　　处：《江西师范大学学报（自然科学版）》2015年第4期331-339,共9页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11271179)资助项目

摘　　要：利用Nevanlinna理论和Wiman-Valiron理论,研究了代数微分方程没有允许解的问题,给出了几类非线性微分方程整函数解的结构,并利用这些结果将Hayman定理推广到微分多项式,综述了在非线性复微分方程及其应用研究中的最新进展.The problem that an algebraic differential equation has no admissible meromorphic solution is studied by using Nevanlinna＇ s theory and Wiman-Valiron theory. The structures of the entire solutions of some nonlinear differential equations are given,and the Hayman＇s theorems to some differential polynomials are extended by using these results. Finally,a survey of his groups＇ recent researches about non-linear complex differential equations and their applications is given.

关 键 词：NEVANLINNA值分布理论 非线性微分方程 微分多项式 亚纯函数解 整函数解 

分 类 号：O175.42[理学—数学]