Uniqueness of meromorphic functions and differential polynomials

Using Nevanlinna value distribution theory, we study the uniqueness of meromorphic functions concerning differential polynomials, and prove the following theorem. Let f(z) and g(z) be two nonconstant meromorphic functions, n(≥ 13) be a positive integer. If fn(f − 1)2f′ and gn(g − 1)2g′ share 1 CM, then f ≡ g.