Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2017, Vol. 34 ›› Issue (1): 31-37.doi: 10.3969/j.issn.1005-3085.2017.01.004

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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).

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

CLC Number: