关于超越亚纯系数微分方程亚纯解的零点

ON THE ZEROS OF MEROMORPHIC SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH TRANSCENDENTAL MEROMORPHIC COEFFICIENTS

本文研究了非齐次线性微分方程的复振荡问题，其中，D0，D1，…，D(k-1)，是超越亚纯函数．当存在某个Ds（1≤s≤k-1）比其它Dj（j≠s）有较快增长的意义下起支配作用时，得到了微分方程（I）亚纯解的零点收敛指数的精确估计式．

In this paper, we investigate the complex oscillation of the differential equationwhere D0, D1,''' , Dk-1, are transcendental meromorphic functions. When there existsa Dd (1 ≤d ≤ k - 1) being dominant in the sense that it has larger growth than any otherDj (j≠ s), we obtain some precise estimates of the exponent of convergence of the zero-sequenceof meromorphic solutions for the above equation.