中文摘要：

对次数至少有一个不小于零的有理函数系数齐次线性微分方程，给出了方程所有亚纯解的级中最大的级的增长性估计，同时对方程的系数为多项式的情形，证明了一个与Hellerstein-Rossi猜想有关的结果．

英文摘要：

This paper gives an estimation of maximal order of all the meromorphic solutions of the homogeneous linear differential equation with rational function coefficients, under the assumption that the degree is greater than or equal to zero for at least one coefficient, and also gives a result which is related to Hellerstein-Rossi conjecture when the coefficients are polynomials.