一类含四个未知函数的方程的非平凡解的存在性的研究

摘要

This paper based on the value distribution theory of meromorphic function, carries out a systematical study on the solutions of functional equation f, (z)+f2 (z)+f3 (z)+f4 (z)=z. In the paper, we will obtained a result as fellow: There is no nonconstant meromorphic functional solutions with order smaller than ~- satisfying the equation f, (z)+fj W+f, (z)+f4 (z)=z.%本文利用亚纯函数值分布论的思想方法,对函数方程f17 1(z)+f17 2(z)f17 3(z)+f17 4(z)=z非平凡解的状况进行研究,得到如下结果:函数方程f17 1(z)+f17 2(z)+f17 3(z)+f17 4(z)=z不存在级小于1/17的非常数亚纯函数解.