On unicity of meromorphic functions when two differential polynomials share one value

Abstract

In this article, we deal with the uniqueness problems of meromorphic functions concerning differential polynomials and prove the following result: Let $f$ and $g$ be two nonconstant meromorphic functions and let $n(\geq 14)$ be an integer such that $n+1$ is not divisible by $3$. If $f^{n}(f^{3}-1)f'$ and $g^{n}(g^{3}-1)g'$ share $(1,2)$ or $``(1,2)"$, then $f\equiv g$. If $\overline{E}_{4)}(1,f^{n}(f^{3}-1)f')=\overline{E}_{4)}(1,g^{n}(g^{3}-1)g')$ and $E_{2)}(1,f^{n}(f^{3}-1)f')=E_{2)}(1,g^{n}(g^{3}-1)g')$, then $f\equiv g$.