| Some Properties of Solutions for Some Types of $Q$-Difference Equations Originated from $Q$-Difference Painlev\'{e} Equation |
| Received:July 22, 2019 Revised:April 23, 2020 |
| Key Words:
meromorphic function $q$-difference equation zero order
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11561033; 11761035), the Natural Science Foundation of Jiangxi Province (Grant No.20181BAB201001) and the Foundation of Education Department of Jiangxi Province (Grant Nos.GJJ190876; GJJ191042; GJJ190895). |
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| Abstract: |
| In this paper, we mainly investigate some properties of meromorphic solutions for several $q$-difference equations, which can be seen as the $q$-difference analogues of Painlev\'{e} equations. Some results about the existence and the estimates of growth of meromorphic solution $f$ for $q$-difference equations are obtained, especially for some estimates for the exponent of convergence of poles of $\Delta_qf(z):=f(qz)-f(z)$, which extends some previous results by Qi and Yang. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2020.05.007 |
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