高阶线性微分方程亚纯解的增长性

On the Growth of Meromorphic Solutions of Higher Order Linear Differential Equations

利用亚纯函数值分布理论,研究了亚纯系数高阶线性微分方程f(k)+Ak-1(z)f(k-1)+…+A0(z)f=0解的增长性,证明了如果A0(z)以∞为亏值,Aj(z)(1≤j≤k-1)满足某些条件,则上述方程的每个非零亚纯解都为无穷级,得到解的超级的下界估计.

The growth of solutions of higher order linear differential equations f（ k）＋ Ak- 1（ z） f（ k- 1）＋ … ＋ A0（ z） f = 0is investigated by using the value distributions theory of meromorphic functions,where Aj（ z）（ 0≤j≤k- 1） are meromorphic functions. It is shown that every nonzero meromorphic solution of such equations has infinite order,provided that A0（ z） has a deficient value ∞ and Aj（ z）（ 1≤j≤k- 1） satisfying certain conditions. The lower bound of hyper order of meromorphic solutions of such equations is also estimated.