一类具指数函数系数的非线性复差分方程  

A Type of Complex Non-linear Difference Equation with Exponential Coefficients

作　　者：周艳萍[1] 郑秀敏[1] ZHOU Yan-ping;ZHENG Xiu-min(Institute of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022)

机构地区：[1]江西师范大学数学与信息科学学院,南昌330022

出　　处：《工程数学学报》2017年第1期31-37,共7页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11301233);江西省自然科学基金(20151BAB201004)~~

摘　　要：众所周知,在复微分方程和复差分方程领域中,Malmquist型方程是比Painlev′e方程和Riccati方程形式更一般的非线性方程.在本文中,我们运用Nevanlinna理论的差分模拟结果和微分域理论对一类具指数函数系数的Malmquist型复差分方程进行了研究.当上述Malmquist型复差分方程的有限级超越亚纯解具有较少的零点和极点时,我们得到其增长性和指数函数ez的增长性一致.该结果是对复微分Malmquist定理和复差分Malmquist定理的推广和补充.It is well known that the non-linear equations of Malmquist type are more general than the Painlev′e equations and the Riccati equations in the field of complex differential equations and complex difference equations. In this paper, by using the difference analogues of Nevanlinna theory and the differential field theory, we investigate one type of complex difference equation of Malmquist type with exponential coefficients. We prove that for any transcendental meromorphic solution to the above complex difference equation of Malmquist type, if it is of finite order and has few zeros and poles, its growth should be of the same rate as that of the exponential function ez. The obtained result generalizes and complements the complex differentialMalmquist Theorem and the complex difference Malmquist Theorem.

关 键 词：非线性复差分方程 指数函数系数 增长性 微分域理论 

分 类 号：O174.52[理学—数学]