Bulletin of the
Korean Mathematical Society BKMS

In this paper, we prove that if $f^nf'-P$ and $g^ng'-P$ share $0$ CM, where $f$ and $g$ are two distinct transcendental meromorphic functions, $n\geq 11$ is a positive integer, and $P$ is a nonzero polynomial such that its degree $\gamma_P \leq 11$, then either $f=c_1e^{cQ}$ and $g=c_2e^{-cQ},$ where $c_1,$ $c_2$ and $c$ are three nonzero complex numbers satisfying $(c_1c_2)^{n+1}c^2=-1,$ $Q$ is a polynomial such that $Q=\int_0^zP(\eta)d\eta,$ or $f=tg$ for a complex number $t$ such that $t^{n+1}=1.$ The results in this paper improve those given by M. L. Fang and H. L. Qiu, C. C. Yang and X. H. Hua, and other authors.

Keywords: meromorphic functions, shared values, differential polynomials, uniqueness theorems

MSC numbers: 30D35, 30D30