数学物理学报(英文版) ›› 1987, Vol. 7 ›› Issue (1): 109-120.

• 论文 • 上一篇    

ON THE GROWTH AND VALUE DISTRIBUTION OF ANALYTIC SOLUTIONS OF A CLASS OF ALGEBRAIC DIFFERENTIAL EQUATIONS

何育赞1, 高仕安2   

  1. 1. Inst. of Math., Academia Sinica, Dept. of Math., South China;
    2. Normal Beijing, China University, Guangzhou, China
  • 收稿日期:1985-09-03 出版日期:1987-03-25 发布日期:1987-03-25
  • 基金资助:
    Projects supported by the Science Fund of the Academy of Sciences.

ON THE GROWTH AND VALUE DISTRIBUTION OF ANALYTIC SOLUTIONS OF A CLASS OF ALGEBRAIC DIFFERENTIAL EQUATIONS

He Yuzan1, Gao Shi'an2   

  1. 1. Inst. of Math., Academia Sinica, Dept. of Math., South China;
    2. Normal Beijing, China University, Guangzhou, China
  • Received:1985-09-03 Online:1987-03-25 Published:1987-03-25
  • Supported by:
    Projects supported by the Science Fund of the Academy of Sciences.

摘要: In this paper, we show that the growth of meromorphic or algebroidal solutions of some algebraic differential equations can be estimated in terms of the growth of the coefficients in tho equation and the counting functions of some value points. We point simulteneously out that the growth of algebroid solutions of certain class of differential equations can be estimated using only the growth of coefficients in the equation, and give an example which is not belonging to this class to show that the above conclusion is not true.

Abstract: In this paper, we show that the growth of meromorphic or algebroidal solutions of some algebraic differential equations can be estimated in terms of the growth of the coefficients in tho equation and the counting functions of some value points. We point simulteneously out that the growth of algebroid solutions of certain class of differential equations can be estimated using only the growth of coefficients in the equation, and give an example which is not belonging to this class to show that the above conclusion is not true.