一阶线性差分方程解的唯一性

Uniqueness for meromorphic solutions of first order linear difference equations

考虑一阶线性差分方程p_(1)(z)f(z+1)+p_(0)(z)f(z)=0和p_(1)(z)f(z+1)+p_(0)(z)f(z)=F(z)亚纯解f(z)的唯一性问题,其中F(z),p_(1)(z)和p_(0)(z)为非零多项式。在f(z)与亚纯函数g(z)CM分担0、1、∞的假设下,给出了f(z)的具体形式。进一步,还研究了方程的两个解CM分担三个值的情形,得到了方程的精确形式和解的具体形式。

The uniqueness problem of the meromorphic solution f(z)to the first order linear difference equations p_(1)(z)f(z+1)+p_(0)(z)f(z)=0 and p_(1)(z)f(z+1)+p_(0)(z)f(z)=F(z)was considered,where,F(z),p_(1)(z)and p_(0)(z)are non-zero polynomials.The specific form of f(z)was provided,under the condition that shares 0,1,∞CM with any meromorphic function g(z).Furthermore,the case where the equation has two solutions sharing three values CM was investigated,leading to the exact form of the equation and the specific form of the solutions.