Uniqueness and value distribution of differences of entire functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:379

Article

Qi, Xiaoguang^1,3  Liu, Kai² 

[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

[2] Nanchang Univ, Dept Math, Nanchang 330031, Jiangxi, Peoples R China

[3] Univ Eastern Finland, Dept Math & Phys, Joensuu 80101, Finland

关键词: Entire functions;    Uniqueness;    Difference;    Shift;    Sharing value;   

DOI  :  10.1016/j.jmaa.2010.12.031

来源: Elsevier

【 摘 要 】

We consider the existence of transcendental entire solutions of certain type of non-linear difference equations. As an application, we investigate the value distribution of difference polynomials of entire functions. In particular, we are interested in the existence of zeros of f(n) (z)(lambda f(m)(z + c) + mu f(m)(z)) - a, where f is an entire function, n, m are two integers such that n >= m > 0, and lambda, mu are non-zero complex numbers. We also obtain a uniqueness result in the case where shifts of two entire functions share a small function. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free