中文摘要：

用Nevanlinna理论,研究差分方程a_1（z）f（qz＋p）＋a_0（z）f（z）=F（z）一个有穷级超越亚纯解f（z）及任一亚纯函数g（z）分担0,1,∞IM时的唯一性问题（其中p,q为常数,满足n∈N~＋,q~n≠±1,q≠0,a_1（z）,a_0（z）,F（z）为非零亚纯函数且级均小于1）,得到了f（z）=g（z）.

英文摘要：

By using Nevanlinna theory,we studied the uniqueness problem for difference equation a_1（z）f（qz＋p）＋a_0（z）f（z）=F（z）when a inite-order transcendental meromorphic solution f（z）and any meromorphic function g（z）were sharing 0,1,∞ IM（where q,p were constants,n∈ N~＋,q~n≠±1,q≠0,a_1（z）,a_0（z）,F（z）were nonzero meromorphic functions and the order was less than1）,we got the result f（z）=g（z）.