| Higher Order Complex Differential Equations with Analytic Coefficients in the Unit Disc |
| Received:March 08, 2019 Revised:May 26, 2019 |
| Key Words:
complex differential equation $[p, q]$-order of growth $[p, q]$-type analytic function unit disc
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| Fund Project: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). |
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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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2020.04.006 |
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