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
基于$q$-差分Painlev\'e方程的几类$q$-差分方程解的性质
Some Properties of Solutions for Some Types of $Q$-Difference Equations Originated from $Q$-Difference Painlev\'{e} Equation
投稿时间:2019-07-22  修订日期:2020-04-23
DOI:10.3770/j.issn:2095-2651.2020.05.007
中文关键词:  亚纯函数  $q$-差分方程  零级
英文关键词:meromorphic function  $q$-difference equation  zero order
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).
作者单位
徐洪焱 上饶师范学院数学与计算机学院, 江西 上饶 334001 
郑秀敏 江西师范大学数学与信息科学学院, 江西 南昌 330022 
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中文摘要:
      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.
英文摘要:
      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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