An extension of Hayman’s alternative to a class of differential polynomials

After a work of W. K. Hayman on the value distribution of a derivative of a meromorphic function, the result is popularly known as Hayman’s alternative, a lot of work is done on the topic. Since a differential polynomial is a natural extension of a derivative, in the paper we prove two results on the value distribution of differential polynomials, which extend some existing results.