非线性微分方程解的唯一性

doi:10.6040/j.issn.1671-9352.0.2019.457

摘要/Abstract

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。

关键词: 亚纯函数, 非线性微分方程, 唯一性, 分担值

Abstract: 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).

Key words: meromorphic function, nonlinear differential equation, uniqueness, shared value

中图分类号:

O174.52

王凌霜,黄志刚. 非线性微分方程解的唯一性[J]. 《山东大学学报(理学版)》, 2019, 54(12): 106-114.

WANG Ling-shuang, HUANG Zhi-gang. Uniqueness of meromorphic solutions of nonlinear differential equations[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(12): 106-114.

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