| 非线性微分方程解的唯一性 |
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| 引用本文： | 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. |
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| 作者姓名： | 王凌霜 黄志刚 |
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| 作者单位： | 苏州科技大学数理学院, 江苏 苏州 215009 |
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| 基金项目： | 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) |
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| 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。
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| 关 键 词： | 亚纯函数 非线性微分方程 唯一性 分担值 |
Uniqueness of meromorphic solutions of nonlinear differential equations |
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| WANG Ling-shuang,HUANG Zhi-gang.Uniqueness of meromorphic solutions of nonlinear differential equations[J].Journal of Shandong University,2019,54(12):106-114. |
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| Authors: | WANG Ling-shuang HUANG Zhi-gang |
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| Institution: | School of Mathmatics and Physics, Suzhou University of Science and Technology, Suzhou 215009, Jiangsu, China |
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| 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). |
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| Keywords: | meromorphic function nonlinear differential equation uniqueness shared value |
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