关于超越亚纯系数微分方程的复振荡

On the Complex Oscillation of Differential Equation with Transcendental Meromorphic Coefficients

在本文中,我们研究了超越亚纯系数非齐次线性微分方程 f^(k)+Af=F(z)的解的复振荡,其中AF≠0是有限级亚纯函数,A是超越的,如果上面的方程存在亚纯函数解f(z),那么最多出现一个有限级亚纯函数解,其它所有亚纯解的增长级和零点收敛指数都为无穷大。

In this paper, we investigate the complex oscillation of a non—homogeneous linear differential equation f^((k))+Af=F where A, F(?)0 are meromorphic functions of finite order and A is transcendental. If the above equation has meromorphic solutions f(z), thenat most one meromorphic solution is of finite order of growth, and other meromorphic solutions are of infinite order of growth, and its exponent of convergence of sequence of zero is infinite.