【摘要】 假设f是Painlevé差分方程■的有穷级非常数亚纯解，其中■和■是关于f的两个多项式，且P（f）与Q（f）互素，它们的系数{a_k},{b_j}均为f的小函数，且a_p?0和b_q?0。再设g是一个非常数的亚纯函数，如果f与g CM分担3个判别的有限值c₁,c₂和c₃,且■,那么f=g。本文主要结果涉及Ablowitz-Halburd-Herbst中的相应结果，研究了非常数的亚纯函数与有关Painlevé方程的非常数的有穷级亚纯解CM分担3个公共值的唯一性问题，并研究了有关Painlevé方程的有穷级非常数亚纯解的值分布问题。更多还原

【Abstract】 Suppose that f is a finite order meromorphic solution of the Painlevé difference equation ■ are relatively prime polynomials in f with the coefficients {a_k},{b_j} being small meromorphic function of f, a_p?0 and b_q?0, and suppose that g is a nonconstant meromorphic function. If f and g share c₁, c₂, c₃ CM, and if ■ ■ for 1≤j≤3, then f=g. The main results in present paper are concerning the corresponding results from Ablowitz-Halburd-Herbst. Moreover, this paper also studies the uniqueness of nonconstant meromorphic functions sharing three values CM with the nonconstant finite order meromorphic solutions of the corresponding Painlevé complex difference equations, and studies the value distribution of the nonconstant finite order meromorphic solutions of the corresponding Painlevé complex difference equations.更多还原