ON ENTIRE SOLUTIONS OF SOME TYPE OF NONLINEAR DIFFERENCE EQUATIONS

doi:10.1016/S0252-9602(18)30786-0

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

ON ENTIRE SOLUTIONS OF SOME TYPE OF NONLINEAR DIFFERENCE EQUATIONS

刘慧芳¹, 毛志强²

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. 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/Abstract

摘要：

In this article, the existence of finite order entire solutions of nonlinear difference equations fⁿ + P_d(z, f)=p₁e^α₁z + p₂e^α₂z are studied, where n ≥ 2 is an integer, P_d(z, f) is a difference polynomial in f of degree d(≤ n-2), p₁, p₂ are small meromorphic functions of e^z, 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:

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

刘慧芳, 毛志强. ON ENTIRE SOLUTIONS OF SOME TYPE OF NONLINEAR DIFFERENCE EQUATIONS[J]. 数学物理学报(英文版), 2018, 38(3): 819-828.

Huifang LIU, Zhiqiang MAO. ON ENTIRE SOLUTIONS OF SOME TYPE OF NONLINEAR DIFFERENCE EQUATIONS[J]. Acta mathematica scientia,Series B, 2018, 38(3): 819-828.

参考文献

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ON ENTIRE SOLUTIONS OF SOME TYPE OF NONLINEAR DIFFERENCE EQUATIONS

ON ENTIRE SOLUTIONS OF SOME TYPE OF NONLINEAR DIFFERENCE EQUATIONS

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