A Polynomial Shared by Certain Differential Polynomials

The principal objective of the paper is to study the uniqueness of meromorphic functions when two differential polynomials share a nonzero polynomial. A result of Yang and Hua (Ann Acad Sci Fenn Math 22:395–406, 1997) is the starting point of this kind of research. In this direction, Majumder (Math Slovaca 67(1):151–164, 2017) proved two results, which contain a major gap in their proofs. In the paper, we not only present a corrected version of the results of Majumder but also provide some improvement of those.