We study the uniqueness theorems of meromorphic functions concerning differential polynomials sharing a nonzero polynomial IM, and obtain two theorems which will supplement two recent results due to X. M. Li and L. Gao.
Let k be a nonnegative integer or infinity. For a ∈ C ∪ {∞} we denote by Ek(a; f) the set of all a-points of f where an a-point of multiplicity m is counted m times if m ≤ k and k + 1 times if m > k. If Ek(a; f) = Ek(a; g) then we say that f and g share the value a with weight k. Using this idea of sharing values we study the uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a nonzero polynomial with finite weight. The results of the paper improve and generalize the related results due to Xia and Xu (2011) and the results of Li and Yi (2011).