Transcendental entire solutions of several Fermat type PDEs and PDDEs with two complex variables

Abstract

This article is concerned with the description of transcendental entire solutions of several Fermat type functional equations in ${ℂ}^2$ concerning partial differential-difference equations and partial differential equations. By utilizing the Nevanlinna theory of meromorphic functions in several complex variables, we establish some results about the existence and the forms of entire solutions for such equations, which are some improvements and generalizations of the previous theorems. Moreover, some examples are given illustrating that our results are precise to some extent.