文献类型：期刊文献

中文题名：一类非线性差分方程亚纯解与亚纯函数分担值的唯一性

英文题名：Uniqueness of Meromorphic Functions Sharing Values with Meromorphic Solutions of Certain Non-linear Difference Equations

作者：陈创鑫[1];张然然[2];陈宝琴[3]

机构：[1]仲恺农业工程学院数学与数据科学学院,广州510025;[2]广东第二师范学院数学学院,广州510303;[3]广东海洋大学数学与计算机学院,广东湛江524088

年份：2025

卷号：46

期号：3

起止页码：321

中文期刊名：数学年刊(A辑)

外文期刊名：Chinese Annals of Mathematics

收录：北大核心2023、、北大核心

基金：广东省特色创新项目(No.2024KTSCX022);国家自然科学基金(No.12101138)的资助。

语种：中文

中文关键词：非线性差分方程;亚纯函数;唯一性

外文关键词：Non-linear difference equations;Meromorphic function;Uniqueness

中文摘要：作者讨论了起源于q-PV方程簇的一类非线性差分方程,其形式为(f(z+1)f(z)-1)(f(z)f(z-1)-1)=M(z)/N(z),其中M(z)和N(z)是两个互异的非零多项式,证明了其有穷级超越亚纯解可由其零点、1值点和极点决定.即,假设f(z)是上述方程的有穷级超越亚纯解,且与亚纯函数g(z)CM分担0,1,∞,那么可得f(z)≡g(z).另外,作者也研究了上述方程当M(z)恒等于N(z)的情形,并得到同样的结论.文中给出的例子说明了所得到两个结论的精确性.

外文摘要：In this paper,the authors discuss a class of nonlinear difference equations,which originated from the q-PV equation family,whose form is(f(z+1)f(z)-1)(f(z)f(z-1)-1)=M(z)/N(z),where M(z)and N(z)are two distinct non-zero polynomials.The authors prove that its transcendental meromorphic solutions with finite order can be determined by their zeros,1 value points,and poles.That is,if f(z)is a transcendental meromorphic solution with finite order of the above equation and sharing 0,1,∞CM with a meromorphic function g(z),then f(z)≡g(z).In addition,the authors also study the case of the above equation where M(z)is identical to N(z),which leads to the same conclusion.Examples for the sharpness of the two conclusions obtained are given in the paper.