title: On a conjecture of R. Brück and some linear differential equations.
abstract: In this paper, we mainly investigate the Brück conjecture concerning entire function f and its differential polynomial [Formula: see text] sharing an entire function [Formula: see text] with [Formula: see text], by using the theory of complex differential equation.
authors.affiliation: Department of Informatics and Engineering, Jingdezhen Ceramic Institute, Jingdezhen, 333403 Jiangxi China.
authors.forename: Hong Yan
authors.initials: HY
authors.lastname: Xu
authors.affiliation: Department of Mathematics, Shandong University, Jinan, 250100 Shandong People's Republic of China.
authors.forename: Lian Zhong
authors.initials: LZ
authors.lastname: Yang
keywords: Brück conjecture; Difference polynomial; Entire function