二阶线性差分方程亚纯解的唯一性  

Uniqueness for Meromorphic Solutions of Second Order Linear Difference Equations

作　　者：张然然[1] 黄志波[2] 陈创鑫 Ran Ran ZHANG;Zhi Bo HUANG;Chuang Xin CHEN(School of Mathematics,Guangdong University of Education,Guangzhou 510303;School of Mathematical Sciences,South China Normal University,Guangzhou 510631;College of Mathematics and Data Science,Zhongkai University of Agriculture and Engineering,Guangzhou 510225,P.R.China)

机构地区：[1]广东第二师范学院数学学院,广州510303 [2]华南师范大学数学科学学院,广州510631 [3]仲恺农业工程学院数学与数据科学学院,广州510225

出　　处：《数学学报（中文版）》2023年第5期855-866,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11801093,11871260);广东省自然科学基金(2018A030313508);广东省普通高校特色创新类项目(2019KTSCX119)。

摘　　要：本文考虑二阶线性差分方程p2(z)y(z+2)+p1(z)y(z+1)+p0(z)y(z)=0的亚纯解f(z)的唯一性,其中p2(z),p1(z),p0(z)是非零多项式,且满足p2(z)+p1(z)+p0(z)■0.在f(z)与任一亚纯函数g(z) CM分担0,1,∞的假设下,给出了f(z)的具体形式.如果g(z)也是方程的解,得到了该方程的精确形式.作为推论,如果亚纯函数g(z)与gamma函数Γ(z) CM分担0,1,∞,则g(z)≡Γ(z).We consider the uniqueness of the meromorphic solution f(z)of the second order linear difference equation p2(z)y(z+2)+pi(z)y(z+1)+p0(z)y(z)=0,where p2(z),pi(z),po(z)are nonzero polynomials with p2(z)+pi(z)+p0(z)■0.We give the forms of f(z)if f(z)shares 0,1,∞ CM with any meromorphic function g(z).Further-more,if g(z)is also a solution of the above equation,we obtain the exact forms of this equation.As a corollary,we see that if a meromorphic function g(z)shares O,1,∞ CM with the gamma function Γ(z),then g(z)=Γ(z).

关 键 词：亚纯函数 差分方程 唯一性 

分 类 号：O174.5[理学—数学]