非线性复微分方程的解与H_ω^∞空间
The Solutions of Nonlinear Complex Differential Equations and H_ω^∞ Space

$利用直接的积分估计，研究非线性复微分方程 $ {\left( {{f^{\left( k \right)}}} \right)^{{n_k}}} + {A_{k - 1}}\left( z \right){\left( {{f^{\left( {k - 1} \right)}}} \right)^{{n_{k - 1}}}} + \cdots + {A_1}\left( z \right){\left( {f'} \right)^{{n_1}}} + {A_0}\left( z \right)f = {A_k}\left( z \right) $ 解的函数空间属性，刻画了方程的解析解，以及它们的导数属于H_ω^∞空间时系数需要满足的条件.改善及推广了已有的相关结果.$
$Based on the straightforward integral estimate, the properties of function spaces of solutions of the nonlinear differential equation $ {\left( {{f^{\left( k \right)}}} \right)^{{n_k}}} + {A_{k - 1}}\left( z \right){\left( {{f^{\left( {k - 1} \right)}}} \right)^{{n_{k - 1}}}} + \cdots + {A_1}\left( z \right){\left( {f'} \right)^{{n_1}}} + {A_0}\left( z \right)f = {A_k}\left( z \right) $ are studied. The sufficient conditions of the coefficients for the derivatives and analytic solutions of the above equation to be in H_ω^∞ are given in this paper, which improves and extends previous results from Huusko-Korhonen-Reijonen.