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 Word: meromorphic function   $q$-difference equation   zero order  
Fund ProjectL: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).
Author NameAffiliation
Hongyan XU School of Mathematics and Computer Science, Shangrao Normal University, Jiangxi 334001, P. R. China 
Xiumin ZHENG Department of Mathematics, Jiangxi Normal University, Jiangxi 330022, P. R. China 
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      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.
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