Characterization of entire solutions of systems of quadratic trinomial difference and partial differential difference equations in $\mathbb{C}^n$

Abstract: In this paper we establish some results about the existence and precise forms of finite order entire solutions of some systems of quadratic trinomial functional equations one of which in $\mathbb{C}^n$, $n\in\mathbb{N}$ and other two in $\mathbb{C}^2$. Our results are the generalizations and improvements of the previous theorems given by Xu-Cao \cite{Xu & Cao & 2018,Xu & Cao & 2020} and Xu-Jiang \cite{Xu Jiang RCSM 2022}. Moreover, we exhibit some examples in support of our claims.