Entire solutions of systems of quadratic trinomial shift and partial differential difference equations in several complex variables

In this paper, we investigate three systems of quadratic trinomial functional equations, focusing on the existence and specific forms of finite-order transcendental entire solutions. Two systems, one formulated in C n Cⁿ with n ∈ N n and the other in C 2 C² , generalize and extend recent results from [Z. Tai, J. Long and X. Xiang, On entire solutions for several systems of quadratic trinomial Fermat type functional equations in C 2 C² , Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 118 (2024), 4, Paper No. 156]. To illustrate the validity and applicability of our findings, we provide concrete examples.