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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2017, Vol. 34 ›› Issue (1): 31-37.doi: 10.3969/j.issn.1005-3085.2017.01.004

• • 上一篇    下一篇

一类具指数函数系数的非线性复差分方程

周艳萍,   郑秀敏   

  1. 江西师范大学数学与信息科学学院，南昌  330022
  • 收稿日期:2015-07-30 接受日期:2016-05-10 出版日期:2017-02-15 发布日期:2017-04-15
  • 通讯作者: 郑秀敏 E-mail: zhengxiumin2008@sina.com
  • 基金资助:
    国家自然科学基金(11301233)；江西省自然科学基金(20151BAB201004).

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

ZHOU Yan-ping,   ZHENG Xiu-min   

  1. Institute of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022
  • Received:2015-07-30 Accepted:2016-05-10 Online:2017-02-15 Published:2017-04-15
  • Contact: X. Zheng. E-mail address: zhengxiumin2008@sina.com
  • Supported by:
    The National Natural Science Foundation of China (11301233); the Natural Science Foundation of Jiangxi Province (20151BAB201004).

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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Painleve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${\rm e}^z$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．

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

Abstract:

It is well known that the non-linear equations of Malmquist type are more general than the Painleve 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 ${\rm e}^z$. The obtained result generalizes and complements the complex differential Malmquist Theorem and the complex difference Malmquist Theorem.

Key words: complex non-linear difference equation, exponential coefficient, growth, differential field theory

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