%0 Journal Article
%T 非线性复微分方程的解与&lt;i&gt;H&lt;/i&gt;&lt;sub&gt;&lt;i&gt;ω&lt;/i&gt;&lt;/sub&gt;&lt;sup&gt;∞&lt;/sup&gt;空间&lt;br&gt;The Solutions of Nonlinear Complex Differential Equations and &lt;i&gt;H&lt;/i&gt;&lt;sub&gt;&lt;i&gt;ω&lt;/i&gt;&lt;/sub&gt;&lt;sup&gt;∞&lt;/sup&gt; Space
%A 孙煜
%A 龙见仁
%A 覃智高
%A 胡光明&lt
%A br&gt
%A SUN Yu
%A LONG Jian-ren
%A QIN Zhi-gao
%A HU Guang-ming
%J 西南大学学报(自然科学版)
%D 2018
%R 10.13718/j.cnki.xdzk.2018.10.014
%X $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&lt;i&gt;H&lt;/i&gt;&lt;sub&gt;&lt;i&gt;ω&lt;/i&gt;&lt;/sub&gt;&lt;sup&gt;∞&lt;/sup&gt;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.$&lt;br&gt;$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 &lt;i&gt;H&lt;/i&gt;&lt;sub&gt;&lt;i&gt;ω&lt;/i&gt;&lt;/sub&gt;&lt;sup&gt;∞&lt;/sup&gt; are given in this paper, which improves and extends previous results from Huusko-Korhonen-Reijonen.
%K 非线性复微分方程
%K Hardy空间
%K 解析解
%K 单位圆&lt
%K br&gt
%K nonlinear complex differential equation
%K Hardy space
%K analytic solution
%K unit disc
%U http://xbgjxt.swu.edu.cn/jsuns/html/jsuns/2018/10/20181014.htm