Higher Order Complex Differential Equations with Analytic Coefficients in the Unit Disc
Received:March 08, 2019  Revised:May 26, 2019
Key Word: complex differential equation   $[p, q]$-order of growth   $[p, q]$-type   analytic function   unit disc  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11861023; 11501142), the Foundation of Science and Technology Project of Guizhou Province (Grant No.[2018]5769-05), the Foundation of Doctoral Research Program of Guizhou Normal University 2016 and the Foundation of Science and Technology of Guizhou Province (Grant No.[2015]2112).
Author NameAffiliation
Sangui ZENG School of Mathematical Science, Guizhou Normal University, Guizhou 550025, P. R. China 
Jianren LONG School of Mathematical Science, Guizhou Normal University, Guizhou 550025, P. R. China 
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Abstract:
      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.
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