系数为亚纯函数的高阶齐次微分方程解的正规性

The regularity of solution of higher order linear differential equations where coefficients are meromorphic functions with finite pole

以复振荡中常用Nevanlinna和Wiman-valiron理论为工具,运用代数体函数的基本理论,借用与之近似的代数方程解的性质来研究微分方程解的正规性.解决了一类系数具有有限个极点的亚纯函数的高阶齐次微分方程解的正规性问题.得出一类具有有限个极点亚纯函数高阶齐次微分方程的解都是正规的,并给出f(z)是超越亚纯解时的结果.

Taken the duplicate vibration in the commonly used Nevanlinna and Wiman-valiron theory as a tool,and utilized the algebra body function the elementary theory,studied the regularity of the differential equation solution with its’ approximate algebraic equation solution nature,solved the question about the regularity of solution of higher order linear differential equations where coefficients are meromorphic functions with finite pole.Obtained the theorem on the regularity of solution of higher order linear differential equations where coefficients are meromorphic functions with finite pole and the result where f（z） is super meromorphic sollution.