On the uniqueness of an entire function sharing a small entire function with some linear differential polynomial

摘要

We prove a theorem on the growth of nonconstant solutions of a linear differential equation. From this we obtain some uniqueness theorems concerning that a nonconstant entire function and its linear differential polynomial share a small entire function. The results in this paper improve many known results. Some examples are provided to show that the results in this paper are the best possible. Keywords entire functions - order of growth - shared values - uniqueness theorems MSC 2000 30D30 - 30D35 Project supported by the NSFC (No. 10771121), the NSF of Shandong Province, China (No. Z2008A01) and the NSFC & RFBR (Joint Project) (No. 10911120056)