单位圆上解析系数的高阶复微分方程

Higher Order Complex Differential Equations with Analytic Coefficients in the Unit Disc

中文关键词:  复微分方程  $[p, q]$级  $[p, q]$型  解析函数

英文关键词:complex differential equation  $[p, q]$-order of growth  $[p, q]$-type  analytic function  unit disc

中文摘要:

      本文研究了下面微分方程$$f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_{1}(z)f'+A_{0}(z)f=0$$解的增长性, 获得了方程解的$[p, q]$级的一些精确估计, 其中$A_{j}(z)$ 为单位圆$\mathbb{D}=\{z:|z|<1\}$上的解析函数, $j=0,1,\ldots,k-1$.

英文摘要:

      The growth of solutions of the following differential equation $$f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_{1}(z)f'+A_{0}(z)f=0$$ is studied, where $A_{j}(z)$ is analytic in the unit disc $\mathbb{D}=\{z:|z|<1\}$ for $j=0,1,\ldots,k-1$. Some precise estimates of $[p, q]$-order of solutions of the equation are obtained by using a notion of new $[p, q]$-type on coefficients.