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]576905), 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). 

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Abstract: 
The growth of solutions of the following differential equation $$f^{(k)}+A_{k1}(z)f^{(k1)}+\cdots+A_{1}(z)f'+A_{0}(z)f=0$$ is studied, where $A_{j}(z)$ is analytic in the unit disc $\mathbb{D}=\{z:z<1\}$ for $j=0,1,\ldots,k1$. 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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