中文摘要：

经典的Nevanlinna理论是研究复微分方程解的性质的有效工具,而Halburd和Korhonen,Chiang和Feng分别给出了差分的对数导数引理的不同版本,在此基础上建立起来的差分的Nevanlinna理论为研究复差分方程,复差分多项式理论提供了理论的基础。主要利用差分的Nevanlinna理论,研究各种类型的非线性的复差分方程的超越整函数解的存在性问题,得到关于几个不同方程解的存在性质的结果,从而把一些复微分方程中的结论推广到了复差分方程中。

英文摘要：

The classical Nevanlinna theory has been extensively applied to investigate the solutions of differential equation.Base on the difference of the lemma of derivative pvopole by Halburd and Korhonen,Chiang and Feng,the difference Nevanlinna theory has been established,which can be used to study the theory of complex difference equations and complex difference polynomials.In this paper,using the basic difference Nevanlinna theory,we derived and obtained some results related to the existence of transcendental entire solutions of different types of nonlinear difference-differential equation.Were extend some results of complex differential equations to complex difference equations.