数学物理学报 ›› 2013, Vol. 33 ›› Issue (4): 759-765.

• 论文 • 上一篇    下一篇

关于代数微分方程亚纯解增长级的Gol'dberg定理的进一步结果

戚建明1,3,4|李叶舟2|袁文俊3,4   

  1. 1.上海电机学院数理教学部 上海 201306|2.北京邮电大学理学院 北京 100876;
    3.广州大学数学与信息科学学院 广州 510006|
    4.广州大学数学与交叉科学广东普通高校重点实验室 广州 510006
  • 收稿日期:2012-02-23 修回日期:2013-07-21 出版日期:2013-08-25 发布日期:2013-08-25
  • 基金资助:

    国家自然科学基金(11271090, 11101048, 10871130, 11171184)、上海高校青年教师培养资助计划(ZZSDJ12020)、广东省自然科学基金(S2012010010121)和上海电机学院重点培育项目(12C104, 12C401, 10XKJ01) 资助

Further Results of Gol'dberg's Theorem Concerning the Growth of Meromorphic Solutions of |Algebraic Differential Equations

 QI Jian-Ming1,3,4, LI Ye-Zhou2, YUAN Wen-Jun3,4   

  1. 1.Department of Mathematics and Physics, Shanghai Dianji University, Shanghai 201306;
    2.School of Science, Beijing University of Posts and Telecommunications, Beijing |100876;
    3.School of Mathematics and Information Sciences, Guangzhou University, |Guangzhou  |510006;
    4.Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou
    University, Guangzhou 510006
  • Received:2012-02-23 Revised:2013-07-21 Online:2013-08-25 Published:2013-08-25
  • Supported by:

    国家自然科学基金(11271090, 11101048, 10871130, 11171184)、上海高校青年教师培养资助计划(ZZSDJ12020)、广东省自然科学基金(S2012010010121)和上海电机学院重点培育项目(12C104, 12C401, 10XKJ01) 资助

摘要:

运用正规族理论, 给出一类高阶代数微分方程 Gol'dberg 定理的进一步推广. 类似地给出了一类特殊的代数微分方程组的亚纯解的增长性估计. 同时举例说明文中的结果是有意义的.

关键词: 亚纯函数, 正规族, 增长级, 代数微分方程组

Abstract:

In this paper, by means of the normal family theory, we give a general estimate result of Gol'dberg's theorem concerning finite growth order of meromorphic solutions of higher order algebraic differential equations. We also estimate the growth order of meromorphic solutions of a type system of a special algebraic differential equations. We also give some
examples to show that our results are interesting.

Key words: Meromorphic function, Normal family, Growth order, Algebraic differential equation system

中图分类号: 

  • 34A20