非线性微分方程解的唯一性  

Uniqueness of meromorphic solutions of nonlinear differential equations

作　　者：王凌霜 黄志刚[1] WANG Ling-shuang;HUANG Zhi-gang(School of Mathmatics and Physics,Suzhou University of Science and Technology,Suzhou 215009,Jiangsu,China)

机构地区：[1]苏州科技大学数理学院

出　　处：《山东大学学报（理学版）》2019年第12期106-114,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11971344);苏州科技大学研究生科研创新计划资助项目(SKCX18-014)

摘　　要：运用Nevanlinna值分布理论,研究亚纯函数的唯一性问题。若f(z)为f′f=F(z)的有限级亚纯解,其中F(z)为非零整函数且λ(F(z))<1,当f(z)与有限级亚纯函数g(z)CM分担0、1、∞,则f=g。如果f(z)为f′+A(z)f^n=F(z)的一个有限级亚纯解,其中A(z)为不等于0的多项式,F(z)为非零整函数且λ(F(z))<1,A(z)≠F(z),若有限级亚纯函数g(z)与f(z)CM分担0、1、∞,则f=g。This paper is devoted to studying the uniqueness of meromorphic functions by Nevanlinna value distribution theory. Obtain that if f(z) is a finite order meromorphic solution of the equation f ′f=F(z) and shares 0、1、∞ with finite order meromorphic function g(z) where F(z) is an entire function and λ(F(z))<1, then f(z)=g(z). If f(z) is a finite order meromorphic solution of the equation f ′+A(z) f ~n=F(z) and shares 0、1、∞ with finite order meromorphic function g(z), where A(z) is a nonzero polynomial and F(z) is an entire function, λ(F(z))<1, A(z)≠F(z), then f(z)=g(z).

关 键 词：亚纯函数 非线性微分方程 唯一性 分担值 

分 类 号：O174.52[理学—数学]