%0 Journal Article
%T 一类线性差分方程的亚纯解与一个亚纯函数分担3个值的唯一性<br>Uniqueness for Meromorphic Solutions Sharing Three Values with a Meromorphic Function to Some Linear Difference Equations
%A 崔宁
%A 陈宗煊
%J 数学年刊（A辑）
%D 2017
%R 10.16205/j.cnki.cama.2017.0002
%X 主要研究差分方程~$a_{1}(z)f(z+1)+a_{0}(z)f(z)=F(z)$~的一个有穷级超越亚纯解 $f(z)$~与亚纯函数~$g(z)$~分担~$0, 1, \infty$~CM~时的唯一性问题~(其中~$a_{1}(z)$, $a_{0}(z), F(z)$~为非零多项式, 且满足~$a_{1}(z)+a_{0}(z)\not\equiv0$), 得到~$f(z)\equiv g(z)$, 或$f(z)+g(z)\equiv f(z)g(z)$, 或存在一个多项式 $\beta(z)=az+b_{0}$~和一个常数~$a_{0}$~满足~$\rme^{a_{0}}\neq \rme^{b_{0}}$,~使得 $f(z)=\frac{1-\rme^{\beta(z)}}{\rme^{\beta(z)}(\rme^{a_{0}-b_{0}}-1)}$~与 $g(z)=\frac{1-\rme^{\beta(z)}}{1-\rme^{b_{0}-a_{0}}}$, 其中~$a(\neq0), b_{0}$~为常数.<br>This paper deals with the uniqueness of a finite-order meromorphic solution $f(z)$ of some linear difference equation $a_{1}(z)f(z+1)+a_{0}(z)f(z)=F(z)$ sharing $0, 1, \infty$ CM with meromorphic function $g(z)$ (where $a_{1}(z)$, $a_{0}(z)$ and $ F(z)$ are nonzero polynomials satisfying $a_{1}(z)+a_{0}(z)\not\equiv0$), and obtain either $f(z)\equiv g(z)$ or $f(z)+g(z)\equiv f(z)g(z)$ or there exists a polynomial $\beta(z)=az+b_{0}$ and a constant $a_{0}$ satisfying $\rme^{a_{0}}\neq \rme^{b_{0}}$, such that $f(z)=\frac{1-\rme^{\beta(z)}}{\rme^{\beta(z)}(\rme^{a_{0}-b_{0}}-1)}$ and $g(z)=\frac{1-\rme^{\beta(z)}}{1-\rme^{b_{0}-a_{0}}}$, where $a(\neq0), b_{0}$ are constants.
%K Meromorphic function
%K Difference equation
%K Shared values
%K Uniqueness&lt
%K br&gt
%K Meromorphic function
%K Difference equation
%K Shared values
%K Uniqueness
%U http://www.camath.fudan.edu.cn/camacn/ch/reader/view_abstract.aspx?file_no=38A102&flag=1