Uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a polynomial

In this paper, we get two uniqueness theorems of meromorphic functions whose certain nonlinear differential polynomials share a polynomial. The results in this paper extend the corresponding results given by Fang (2002) in [7]. Our reasoning in this paper will correct a defective reasoning in the proof of Theorem 4 in Bhoosnurmath and Dyavanal (2007) [8]. An example is provided to show that some conditions of the main results in this paper are necessary.