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.