中文摘要：

研究齐次线性微分方程f^（k）＋ak-1（z）f^（k-1）＋…＋a1（z）f′＋a0（z）f=0,（k∈N）的有穷级解,其中系数是单位圆D={z：｜z｜〈1}内解析函数。推广了D.Benbourenane和L.R.Sons的一个结果,并利用J.Heittokangas,R.Korhonen和J.Rattya的一个估计式得到了方程解的增长估计的上界,部分改进了Chen Z.X和K.H.Shon的一个结果。

英文摘要：

The finite-ovder solutions of the homogenous linear differential equation f（k）＋ak-1（z）f（k-1）＋…＋a1（z）f′＋a0（z）f=0,（k∈N）,were investigated,where the coeffiences were set to be analytic in the unit disc Δ={z：｜z｜1}.It extended the result of D.Benbourenane and L.R.Sons,and obtained an upper bound of the order of the solutions by making use of the estimation from J.Heittokangas,R.Korhonen and J.Rtty,which in part improved the result of Z.X.Chen and K.H.Shon.