Uniqueness of meromorphic functions and nonlinear differential polynomials sharing a nonzero polynomial (Q2810992)

This paper studies a uniqueness question of meromorphic functions any two of which certain nonlinear differential polynomials \(\bigl (f^n(af^m+b)\bigr)^{(k)}\) and \(\bigl (g^n(ag^m+b)\bigr)^{(k)}\) share a nonzero polynomial \(P\). The results in this paper improve and extend the corresponding results from the paper \textit{X-M. Li} and \textit{H-X. Yi} [Comput. Math. Appl. 62, No. 2, 539--550 (2011; Zbl 1228.30024)]. The analysis and the reasoning of the present paper is new and deep.