A study on the existence of solutions for the class of nonlinear partial differential-difference equations in several complex variables

We explore the non-existence and existence of transcendental entire solutions of a certain type of partial differential-difference equations in Cn of the type defined by Fermat with finite-order constraint. We also study the existence as well as the form of transcendental entire solutions for a particular class of Fermat's type partial differential-difference equations in C2 with finite-order constraint. The results provided as solutions for these problems have substantially enhanced the theorem that was previously suggested by Xu, Cao, Liu, Wang, Zhang, Zheng [22, 32, 33, 37, 40]. In contrast to earlier articles, this one uses a different technique. By using several examples, it is shown that there are certain conditions and types of transcendental entire solutions of finite order of such equations.