数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (3): 733-739.doi: 10.1016/S0252-9602(16)30035-2

• 论文 • 上一篇    下一篇

ON ALGEBRAIC SOLUTIONS OF THE SECOND-ORDER COMPLEX DIFFERENTIAL EQUATIONS WITH ENTIRE ALGEBRAIC ELEMENT COEFFICIENTS

孔荫莹1, 郭晓晶2, 孙道椿3   

  1. 1. School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou 510320, China;
    2. Sontan College, Guangzhou University, Guangzhou 511370, China;
    3. School of Mathematics Science, South China Normal University, Guangzhou 510631, China
  • 收稿日期:2015-04-02 修回日期:2015-04-02 出版日期:2016-06-25 发布日期:2016-06-25
  • 通讯作者: Daochun SUN,E-mail:sundch@scnu.edu.cn E-mail:sundch@scnu.edu.cn
  • 作者简介:Yinying KONG,E-mail:kongcoco@hotmail.com;Xiaojing GUO,E-mail:betty0104@sina.com
  • 基金资助:

    The Project Supported by Guangdong Natural Science Foundation (2015A030313628, S2012010010376), Training plan for Distinguished Young Teachers in Higher Education of Guangdong (Yqgdufe1405), Guangdong Education Science Planning Project (2014GXJK091, GDJG20142304) and the National Natural Science Foundation of China (11301140, 11101096).

ON ALGEBRAIC SOLUTIONS OF THE SECOND-ORDER COMPLEX DIFFERENTIAL EQUATIONS WITH ENTIRE ALGEBRAIC ELEMENT COEFFICIENTS

Yinying KONG1, Xiaojing GUO2, Daochun SUN3   

  1. 1. School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou 510320, China;
    2. Sontan College, Guangzhou University, Guangzhou 511370, China;
    3. School of Mathematics Science, South China Normal University, Guangzhou 510631, China
  • Received:2015-04-02 Revised:2015-04-02 Online:2016-06-25 Published:2016-06-25
  • Contact: Daochun SUN,E-mail:sundch@scnu.edu.cn E-mail:sundch@scnu.edu.cn
  • Supported by:

    The Project Supported by Guangdong Natural Science Foundation (2015A030313628, S2012010010376), Training plan for Distinguished Young Teachers in Higher Education of Guangdong (Yqgdufe1405), Guangdong Education Science Planning Project (2014GXJK091, GDJG20142304) and the National Natural Science Foundation of China (11301140, 11101096).

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摘要：

The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coefficients. Several theorems on the existence of solutions are obtained, which perfect the solution theory of linear complex differential equations.

关键词: complex differential equations, entire algebraic function elements, algebraic solutions

Abstract:

The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coefficients. Several theorems on the existence of solutions are obtained, which perfect the solution theory of linear complex differential equations.

Key words: complex differential equations, entire algebraic function elements, algebraic solutions

中图分类号: 

  • 30D35
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