Unicity on entire function concerning its differential polynomials in Several complex variables

In this paper, we study the uniqueness of the differential-difference polynomials of entire functions. We prove the following result: Let $f(z)$ be a non-constant entire function, let $g(z)$ be a differential polynomials of $f$ as define in (1.2), and let $a_{1}, a_{2}$ be two distinct finite complex numbers. If $f(z)$ and $g(z)$ share $a_{1}$ CM, and $a_{2}$ IM. Then either $f(z)\equiv g(z)$ or $$f(z)\equiv a_{2}+(a_{1}-a_{2})(e^{p(z)}-1)^{2},$$ and $$g(z)\equiv a_{1}+(a_{1}-a_{2})(e^{p(z)}-2),$$ where $p(z)$ is a non-constant entire function on $\mathbb{C}^{n}$. In fact, it is easy to see that if we replace $a_{1}$ and $a_{2}$ by two distinct small functions of $f(z)$, the result of above still holds.Comment: arXiv admin note: substantial text overlap with arXiv:2012.1377