数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (3): 819-828.doi: 10.1016/S0252-9602(18)30786-0

• 论文 • 上一篇    下一篇

ON ENTIRE SOLUTIONS OF SOME TYPE OF NONLINEAR DIFFERENCE EQUATIONS

刘慧芳1, 毛志强2   

  1. 1. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China;
    2. School of Mathematics and Computer, Jiangxi Science and Technology Normal University, Nanchang 330038, China
  • 收稿日期:2017-03-14 修回日期:2017-10-20 出版日期:2018-06-25 发布日期:2018-06-25
  • 作者简介:Huifang LIU,E-mail:liuhuifang73@sina.com;Zhiqiang MAO,E-mail:maozhiqiang1@sina.com
  • 基金资助:

    This work is supported by the National Natural Science Foundation of China (11661044).

ON ENTIRE SOLUTIONS OF SOME TYPE OF NONLINEAR DIFFERENCE EQUATIONS

Huifang LIU1, Zhiqiang MAO2   

  1. 1. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China;
    2. School of Mathematics and Computer, Jiangxi Science and Technology Normal University, Nanchang 330038, China
  • Received:2017-03-14 Revised:2017-10-20 Online:2018-06-25 Published:2018-06-25
  • Supported by:

    This work is supported by the National Natural Science Foundation of China (11661044).

摘要:

In this article, the existence of finite order entire solutions of nonlinear difference equations fn + Pd(z, f)=p1eα1z + p2eα2z are studied, where n ≥ 2 is an integer, Pd(z, f) is a difference polynomial in f of degree d(≤ n-2), p1, p2 are small meromorphic functions of ez, and α1, α2 are nonzero constants. Some necessary conditions are given to guarantee that the above equation has an entire solution of finite order. As its applications, we also find some type of nonlinear difference equations having no finite order entire solutions.

关键词: Nevanlinna theory, difference polynomial, difference equation, entire solution

Abstract:

In this article, the existence of finite order entire solutions of nonlinear difference equations fn + Pd(z, f)=p1eα1z + p2eα2z are studied, where n ≥ 2 is an integer, Pd(z, f) is a difference polynomial in f of degree d(≤ n-2), p1, p2 are small meromorphic functions of ez, and α1, α2 are nonzero constants. Some necessary conditions are given to guarantee that the above equation has an entire solution of finite order. As its applications, we also find some type of nonlinear difference equations having no finite order entire solutions.

Key words: Nevanlinna theory, difference polynomial, difference equation, entire solution