非线性微分-差分方程的解
SOLUTIONS OF NONLINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS

本文研究了非线性微分-差分方程f（z）n+an-1f（z）n-1+…+a1f（z）+q（z）eQ（z）f（k）（z+c）=P（z）的有穷级非零整函数解的增长性和零点分布问题.利用微分-差分Nevanlinna值分布的方法，获得了当方程的系数满足一定条件时，方程解的增长性估计和零点分类.特别地，当n=2，a1≠0指数多项式解满足某些条件时，获得了解具有特别的形式.该结果推广了先前文献[1，2]的结果.
In this paper, we study the growth and distribution of zeros of entire solutions of finite order of nonlinear differential-difference equation f(z)n+an-1f(z)n-1+…+a1f(z)+q(z)eQ(z)f(k)(z+c)=P (z). By using the differential-difference Nevanlinna values distribution theory, we obtain an estimation of the growth and the distribution of zeros of solutions of the differential-difference equation if there are some attached condiction on the coefficients. Particularly, when n=2 and a1≠0, we obtain that exponential polynomial solutions satisfying some condictions must reduce to rather specific forms, which improves the results of [1, 2]