一类差分方程的亚纯解与亚纯函数分担3个值的唯一性

Unicity for Meromorphic Solutions of Some Difference Equations Sharing Three Values with Any Meromorphic Functions

摘要: 利用亚纯函数的Nevanlinna值分布理论和分类讨论的思想方法, 研究了差分方程a1(z)f(z+1)+a0(z)f(z)=0的有穷级亚纯解f(z)与任一亚纯函数g(z)分担0, 1, CM时的唯一性问题, 得到f(z)g(z)或者f(z)g(z)1, 其中a1(z)和a0(z)是非零多项式且满足a1(z)+a0(z)0.

Abstract: 〖JP3〗By utilizing Nevanlinna's value distribution theory of meromorphic functions and categorized discussion method, the uniqueness of a finite-order meromorphic solution f(z) of the difference equation a1(z)f(z+1)+a0(z)f(z)=0 〖JP+1〗sharing 0, 1, 〖KG-1mm〗CM with any meromorphic function g(z) is investigated, and the result is given that f(z)〖JP2〗g(z) or f(z)g(z)1 under the above condition, where a1(z) and a0(z) are nonzero polynomials satisfying a1(z)+a0(z)0.〖JP〗