Uniqueness Problems Of Meromorphic Functions

In 1925, R. Nevanlinna established two fundamental theorems of meromorphic functions and the study of the value distribution theory of modern times started. Several decades, the further and new development of the value distribution of meromorphic functions would always be based on Nevanlinna's theory. In this paper, based on Nevanlinna's theory, some problems in the uniqueness theory of meromorphic functions can be studied. Also, the whole paper is divided into six chapters.The first chapter of the paper starts from the preliminary and some basic theorems and results in Nevanlinna's theory of meromorphic functions.In Chapter 2 we discuss the uniqueness problems of the derivatives of meromorphic functions that share four small functions, which improves some results given by G. D. Qiu, W. J. Yuan and so on. Moreover, we resolve one conjecture posed by P. Li etc.In Chapter 3 we are mainly concerned with the uniqueness problems of a meromorphic function and its differential polynomial sharing two or three small functions, which generalizes some results given by G. D. Qiu and so on. Moreover, the examples show the condition of our results is necessary.In Chapter 4 we investigate the uniqueness problems of a entire function and its differential polynomial sharing one small function, which extends some results obtained by R. Br(u|¨)ck, H. L. Qiu, Amer H. H. Al-khaladi and so forth.In Chapter 5, using the idea of weighted sharing, we prove some results on uniqueness of meromorphic functions that share three values with one shared value for their derivatives, which improve some results given by K. Tohge, Amer H. H. Al-khaladi etc.In the last part of the paper we deal with the uniqueness problems of meromorphic functions that share five small functions, which generalize and improve some results obtained by Nevanlinna, Y. H. Li, J. Y. Qiao and so on.