On the entire solutions for several partial differential difference equations (systems) of Fermat type in C2

By utilizing the Nevanlinna theory of meromorphic functions in several complex variables, we will establish some theorems about the existence and the forms of entire solutions for several partial differential difference equations (systems) of Fermat type with two complex variables such as F(z)(2) + [f(z + c) + partial derivative f/partial derivative z(1) + partial derivative f/partial derivative z(2)](2) = 1 and {f(1)(z)(2) + [f(2)(z + c) + partial derivative f(1)/partial derivative z(1) + partial derivative f(1)/partial derivative z(2)](2) = 1, f(2)(z)(2) + [f(1)(z + c) + partial derivative f(2)/partial derivative z(1) + partial derivative f(2)/partial derivative z(2)](2) = 1, which are some extensions and generalizations of the previous theorems given by Xu and Cao [29,30], Xu, Liu and Li [28], and Liu, Yang [18-20]. Moreover, we give some examples to explain that our results are precise to some extent.