数学物理学报 ›› 2011, Vol. 31 ›› Issue (6): 1610-1618.

• 论文 • 上一篇    下一篇

二阶线性微分方程亚纯解与小函数的关系

黄志刚   

  1. 苏州科技学院数理学院 |江苏苏州 215009
  • 收稿日期:2010-12-21 修回日期:2011-12-15 出版日期:2011-12-25 发布日期:2011-12-25
  • 基金资助:

    国家自然科学基金(11001057)、江苏省自然科学基金(BK2010234)和江苏省青蓝工程资助

The Relation Between Meromorphic Solutions of Second Order Differential Equations and Functions of Small Growth

HUANG Zhi-Gang   

  1. School of Mathematics and Physics, Suzhou University of Science and Technology, Jiangsu Suzhou 215009
  • Received:2010-12-21 Revised:2011-12-15 Online:2011-12-25 Published:2011-12-25
  • Supported by:

    国家自然科学基金(11001057)、江苏省自然科学基金(BK2010234)和江苏省青蓝工程资助

摘要:

该文讨论二阶线性微分方程f''+A(z)f=0, 其中A(z)是具有至多有穷多个极点的超越亚纯函数, 得到了上述方程的亚纯解以及它的一阶, 二阶导数和小函数的关系.

关键词: 线性微分方程, 亚纯函数, 零点收敛指数, 小增长函数

Abstract:

This article is devoted to studying the second order differential equation f''+A(z)f=0, where A(z) is a meromorphic function with at most finitely many poles. The relation between functions of small growth and meromorphic solutions, their 1st and 2nd derivatives of the above equation are obtained.

Key words: Linear differential equation, Meromorphic function, Exponent of convergence of zero-sequence, Function of small growth

中图分类号: 

  • 34M10