理论数学

Vol.1 No.3 (October 2011)

一类微分方程解和小函数的关系
The Relation between Solutions of a Class of Differential Equations with Functions of Small Growth

 

作者:

刘薇 , 陈宗煊

 

关键词:

微分方程整函数小函数收敛指数Differential Equation Entire Function Function of Small Growth Exponent of Convergence

 

摘要:

在文中研究了微分方程f"+A1f'+A0f=0 f"+ A0f=0的解以及它们的一阶导数与小函数的关系,其中A0A1是不恒为零的有限级整函数,其零点收敛指数小于其增长级,且A0/A1的增长级等于A0A1增长级的最大值。In this paper, we investigate the relation between solutions, their 1st derivatives of equationsf"+A1f'+A0f=0 and f"+A0f=0 and functions of small growth, where A0,A1are entire functions with finite orders and not identically zero.

The exponent of convergence of the zero-sequence of Aj is less than the order of Aj, and the order of A0/A1 equals the maximum of the orders of A0 and A1.




文章引用:

刘薇 , 陈宗煊 (2011) 一类微分方程解和小函数的关系。 理论数学, 1, 177-183. doi: 10.12677/pm.2011.13035

 

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