Entire solutions for some Fermat type functional equations concerning difference and partial differential in ℂ2

The main purpose of this paper is concerned with the existence and the forms of transcendental entire solutions of several Fermat type functional equations concerning difference and partial differential in ℂ2, by utilizing the Nevanlinna theory of meromorphic functions in several complex variables. Some results are obtained to give the forms of entire solutions for such equations, which are some improvements and generalizations of the previous theorems given by Xu and Cao, Liu and Dong. Moreover, some examples are given to show that there are great differences in the forms of transcendental entire solutions with finite order of Fermat type functional equations between in several complex variables and in a single complex variable.