中文摘要：

本文研究高阶线性微分方程f~（（k））＋A_（k-1）f~（（k-1））＋···＋A1f′＋A0f=0解的增长性,其中Aj（j=0,···,k-1）为整函数.当存在某个系数A_s是方程ω′′＋P（z）ω=0的一个非零解时,我们得到上述方程具有无穷级解的判定条件,并对解的超级进行了估计.这里的P（z）为非零多项式,当P（z）为特定形式的多项式时,A_s可取为Airy函数,Weber-Hermite函数或指数函数.

英文摘要：

In this paper, we investigate the growth of solutions to higher order linear differential equation f（k） ＋ Ak-1f（k-1） ＋... ＋ Aof =0, where Aj（j = 0,... ,k - 1） are entire functions. When there exists some coefficient As being a nonzero solution of ω＂ ＋ P（z）ω -= 0, where P（z） is a non-constant polynomial, we obtain some conditions to guarantee that every nontrivial solution of the above equation has infinite order. We also obtain some estimation on hyper-order of its solutions. When the polynomial P（z） takes some special expression, As may be an Airy function, Weber-Hermite function or exponential function.