复微分-差分方程组的超越解 献给余家荣教授100华诞  

Transcendental solutions of systems of complex differential-difference equations

作　　者：刘曼莉 高凌云[2] Manli Liu;Lingyun Gao

机构地区：[1]山东大学数学学院,济南250100 [2]暨南大学数学系,广州510632

出　　处：《中国科学：数学》2019年第11期1633-1654,共22页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11271161)资助项目

摘　　要：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.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.

关 键 词：微分-差分方程 超越函数 解的性质 

分 类 号：O1[理学—数学]