| In this thesis, we investigate the complex oscillation properties of the solutions of some types of linear differential equations by applying the theories and methods of complex analysis. It contains following five contains.In part one, we give a brief introduction of history on development of this research field.In part two, we introduce some preliminary knowledge, which is mainly definitions and marks of some concepts used in later chapters.In part three, with the help of my teacher , we investigated the growth of solutions of is a non-constant polynomial and is an entire function of The following is obtained: any solution of the above equation satisfy which generalizes some results of Yang Lianzhong and Wang Jun et al; in addition , we investigate the transcendental solutions of a certain type of nonlinear differential equations such as where is an entire function of order less than 1, are nonzero constants. a (z)b1,b2In part four, the value distribution of differential polynomials is studied . The results in this part improve and generalize some previous theorems given by Yang Chungchun ( On deficiencies of differential polynomials, Math. Z., 116(1970)), (197-204), H. Gopalakrishna and S.S.Bhoosnurmath (On distribution of values of differential polynomials , Indian J. Pure Appl. Math. , 17(1986), 367-372), I. Lahiri (A note on distribution of nonhomogeneous differential polynomials , Hokkaido Math. J., 21(2002), 453-458) and Yi Hongxun (On zeros of differential polynomials, Adu. In Math., 18(1989), 335-351) et al .Examples show that the results in this paper are sharp.In part five, I deal with the problem of uniqueness of meromorphic functions concerning their derivatives that sharing one small function,we improve some results of Xiong and obtain the following results: Let f and g be two transcendental meromorphic functions and a (≠0,∞) be a small function with respect to f and g. Suppose that Where m , n ,k are positive integers. non-constant meromorphic function.
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