一类非线性微分差分方程亚纯解的性质

利用值分布理论，研究了几类非线性差分方程是否有有限级的超越亚纯解的问题，还考虑了:微分差分方程$~f^{n}(z)+M(z,f)=h(z)$是否存在有限级超越整函数解的问题，其中$~n\geq3$是整数， $~h(z)$是非零的有理函数，$~M(z,f)$是系数为小函数的线性微分差分多项式.

Property of Meromorphic Solutions of Certain Nonlinear Differential and Difference Equations

By applying Nevanlinna’s value distribution theory of meromorphic functions,the following problems are investigated: the existence of finite order transcendental meromorphic solutions of several kinds nonlinear difference equations,and the existence of finite order transcendental entire function solutions of differential-difference equations with the form f n(z)+M(z,f)=h(z),where n(≥3) is an integer,h(z) is a given non-vanishing rational function,and M(z,f) is a linear differential-difference polynomial in f.