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

主要研究差分方程a_1(z)f(x+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,∞CM时的唯一性问题(其中a_(z),a0(z),F(z)为非零多项式,且满足a_1(z)+a_0(z)■0),得到f(x)≡g(z),或f(z)+g(z)≡f(z)g(z),或存在一个多项式β(z)=az+b_0和一个常数a_0满足e~(a_0)≠e~(b_0),使得f(z)=(1-e~(β(x)))/(e~(β(x))(e~(a_o-b_0)-1))与g(z)=(1-e~(β(x)))/(1-e~(b_o-a_0)),其中a(≠0),b_0为常数.

Uniqueness for Meromorphic Solutions Sharing Three Values with a Meromorphic Function to Some Linear Difference Equations

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.