On Entire Solutions of Two Certain Types of Quadratic Trinomial PDDEs with Two Complex Variables

In this article, we study the existence and specific form of finite order transcendental entire solutions of two certain types of quadratic trinomial PDDEs(partial differential difference equations), including first-order and second-order nonlinear PDDEs in \(\mathbb {C}^2\) , which extend the previous results. Furthermore, some examples are exhibited to illustrate our results.