| 基于$q$-差分Painlev\'e方程的几类$q$-差分方程解的性质 |
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| 引用本文： | 徐洪焱,郑秀敏.基于$q$-差分Painlev\''e方程的几类$q$-差分方程解的性质[J].数学研究及应用,2020,40(5):507-518. |
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| 作者姓名： | 徐洪焱 郑秀敏 |
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| 作者单位： | 上饶师范学院数学与计算机学院, 江西 上饶 334001;江西师范大学数学与信息科学学院, 江西 南昌 330022 |
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| 基金项目： | 国家自然科学基金(Grant Nos.11561033; 11761035）,江西省自然科学基金(Grant No.20181BAB201001), 江西省教育厅科学研究资助项目(Grant Nos.GJJ190876; GJJ191042; GJJ190895). |
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| 摘 要： | 文章讨论了几类$q$-差分Painlev\''e方程的亚纯解性质,获得了方程亚纯解的存在性条件、增长级的估计,以及亚纯解$f$的$q$-差分$\Delta_qf(z):= f(qz)-f(z)$的极点收敛指数的估计等结果,进一步推广了Qi-Yang的结果.
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| 关 键 词： | 亚纯函数 $q$-差分方程 零级 |
| 收稿时间： | 2019/7/22 0:00:00 |
| 修稿时间： | 2020/4/23 0:00:00 |
Some Properties of Solutions for Some Types of $Q$-Difference Equations Originated from $Q$-Difference Painlev\'{e} Equation |
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| Hongyan XU,Xiumin ZHENG.Some Properties of Solutions for Some Types of $Q$-Difference Equations Originated from $Q$-Difference Painlev\''{e} Equation[J].Journal of Mathematical Research with Applications,2020,40(5):507-518. |
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| Authors: | Hongyan XU Xiumin ZHENG |
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| Institution: | School of Mathematics and Computer Science, Shangrao Normal University, Jiangxi 334001, P. R. China; Department of Mathematics, Jiangxi Normal University, Jiangxi 330022, P. R. China |
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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. |
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| Keywords: | meromorphic function $q$-difference equation zero order |
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