复微分-差分方程组的超越解 献给余家荣教授100华诞

本文利用复差分值分布理论和复微分方程理论,将复差分方程和微分方程结合起来,首先研究一类复高阶微分-差分方程超越整函数解,给出其超越整函数解的具体形式.其次,进一步考虑更为复杂的两类复微分-差分方程组超越整函数解的形式以及微分-差分方程组解的存在性问题,得到在一定条件下不存在超越整函数解的结论,例子表明本文定理中的条件是精确的.第三,讨论一类复微分-差分方程组,得到关于解的增长级的一个结果.最后,讨论一类复高阶?差分微分-函数方程超越亚纯解的特征函数,在对其系数的特征函数给出限制时,得到其超越亚纯解的特征估计,例子也表明本文的条件是精确的.

Transcendental solutions of systems of complex differential-difference equations

In this paper, by using Nevanlinna value distribution theory, complex differential theory and combining the difference equations with differential equations, firstly we investigate the form of transcendental entire solutions on a type of complex higher-order differential-difference equations;some specific solutions are given.Secondly, we further consider the existence or the form of solutions on types of systems of differential-difference equations;some results are obtained. Thirdly, we discuss the growth of solutions on a class of systems of complex differential-difference equations. Finally, we consider the characteristic functions of transcendental meromorphic solutions on a type of complex ? difference-functional composite equations. When proper limitation of the characteristic functions on coefficients are given, the characteristic functions can be estimated;an example also shows that the condition in our theorem is precise.