In this paper, we investigate uniqueness problems of differential polynomials of meromorphic functions. Let a, b be non-zero constants and let n, k be positive integers satisfying n ≥ 3k ＋ 12. If f^n＋ af^（k）and g^n＋ ag^（k）share b CM and the b-points of f^n＋ af^（k）are not the zeros of f and g, then f and g are either equal or closely related.
In this paper, we investigate the growth of the meromorphic solutions of the following nonlinear difference equations F（Z）N＋pN-1（F）=0,where n ≥ 2 and small functions as proposed by Yang than 1. Pn-1（f） is a difference polynomial of degree at most n - 1 in f with coefficients. Moreover, we give two examples to show that one conjecture and Laine [2] does not hold in general if the hyper-order of f（z） is no less
