标题:
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
关键字:
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
期刊名称:
《Pure Mathematics》, Vol.1 No.3, 2011-10-31
摘要:
在文中研究了微分方程f"+A1f'+A0f=0和 f"+ A0f=0的解以及它们的一阶导数与小函数的关系,其中A0和A1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A0和A1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.