Uniqueness Of Meromorphjc Functions Concerning Differential Polynomials

For the better part of the past half-century, Nevanlinna theory is highly devel-oped, one important aspect is the introduction of derivatives, combined with the function to consider the value distribution problem. Differential polynomial value distribution theory is an important subject of the value distribution theory. In 1959, W.K.Hayman proposed the famous Hayman problem. After it, many mathemat-ical had done a lot of work on the research of Hayman problem. In 1996, Fang Ming Liang and Hua Xin Hou received the uniqueness results corresponding to the Hayman problem, proved that the uniqueness theorem of entire functions fnf(?) con-cerning sharing one value. Afterwards, many mathematicians such as C.C.Yang and Yi Hong-xun studied on the subject successively, and established a series of interesting uniqueness theorem. These works actived the subject about differential polynomials involving meromorphic function. On this basis, this paper studies the uniqueness of sharing fixed points, rational function and sharing-set.This paper is divided into four sections:In section one, we mainly introduce the basic Nevanlinna theory and some classical theory of the uniqueness results.In section two, we are mainly devoted to the uniqueness problems on mero-morphic functions and its differential polynomials sharing rational function, which generalize the results of Lin and Yi, Yang and Qi.In section three, we are mainly concerned with the uniqueness problems of entire functions and its differential polynomials sharing one finite set with multiplicity≤κ. We improve some former results given by Li and Li, Lin and Zhang.In section four, we are mainly presented some problems.