Entire solutions of several quadratic binomial and trinomial partial differential-difference equations in C2

An equation is called a complex partial differential-difference equation, if this equation includes partial derivatives, shifts, or differences of complex-valued functions f , which can be called PDDE for short and a functional equation of the form f n + g n = 1 , where n is an integer, is called the Fermat-type equation. In this paper, we study the existence and the precise form of finite order transcendental entire solutions of several Fermat-type PDDEs and quadratic trinomial functional equations in C 2 . The main results of the paper generalize several existing results in this direction. In addition, we exhibited by several examples that our results are precise to some extent.