慢增长系数齐次线性微分方程解的性质

The Properties of Solutions of Homogeneous Linear Differential Equations with Coefficients of Small Growth

研究了慢增长亚纯系数齐次线性微分方程亚纯解的零点收敛指数,得到了这类方程具有零点收敛指数为有穷的线性无关的超越解的最大个数。

In this paper,we investigate the exponents of convergence of the zero sequence of meromorphic solutions of homogeneous linear differential equations with meromorphic coefficients of small growth,and obtain that this type of equations are of maximum number of linear independent transcendental solutions that its exponents of convergence of the zero sequence are finite,and that this type of equations are of minimun number of solutions that its exponents of convergence of the zero sequence are infinite in a fundamental solution set.