| 关于代数微分方程(f')~n=R(z,f)的亚纯解 |
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| 引用本文： | 袁文俊,李叶舟.关于代数微分方程(f')~n=R(z,f)的亚纯解[J].数学学报,2001,44(2):277-286. |
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| 作者姓名： | 袁文俊 李叶舟 |
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| 作者单位： | [1]广州大学桂花岗校区数学系,广东广州510405 [2]中国科学院数学与系统科学研究院数学研究所,北京100080 |
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| 基金项目： | 国家自然科学基金资助项目(19971091);原广州师院科研资助项目 |
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| 摘 要： | 在本文中,我们首先考虑了具有理系数的代数微分方程（ｆ＇）ｎ＝Ｒ（ｚ,ｆ）亚 纯解的个数估计问题,并举例说明所得结果是精确的．其次,我们运用 Ｎｅｖａｎｌｉｎｎａ值 分布论,讨论了具亚纯系数的典型代数微分方程（ｆ＇）３＝ａ０（ｆ－ τ１）２（ｆ－ τ２）２（ｆ－ τ３）２ 的可分解亚纯解．文中的结果推广或改进了高仕安［１］,Ｇｕｎｄｅｒｓｅｎ Ｇ．和ＬａｉｎｅＩ［２］以 及何育赞, ＬａｉｎｅＩ．［３－５］等人的工作．
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| 关 键 词： | 代数微分方程 亚纯解 Nevanlinna值分布论 |
| 文章编号： | 0583-1431(2001)02-0277-10 |
| 修稿时间： | 1999年6月22日 |
On Meromorphic Solutions of Algebraic Differentical Equation (f')~n = R(z, f) |
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| YUAN Wen Jun.On Meromorphic Solutions of Algebraic Differentical Equation (f')~n = R(z, f)[J].Acta Mathematica Sinica,2001,44(2):277-286. |
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| Authors: | YUAN Wen Jun |
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| Institution: | YUAN Wen Jun (Department of Mathematics, Guihuagang School District, Guangzhou University, Guangzhou 510405, P. R. China) LI Ye Zhou (Institute of Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, P. R. |
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| Abstract: | In this paper, we first investigate the number of meromorphic solutions of algebraic differential equation (f')" = R(z,f) with rational coefficients and give examples to show its precise. Secondly, applying Nevanlinna distribution theories, we consider solutions of a typical algebraic differential equation (f')3 = a0(f - τ1)2(f- τ2)2(f-τ3)2. Results in this paper improve others, such as by Gao shi'an 1], Gundersen G. and Laine I2], He Yuzan and Laine I.3-5]. |
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| Keywords: | Algebraic differential equation Meromorphic solution Nevanlinna distri- bution theories |
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