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

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

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.