Abstract.

This article is devoted to explore the entire solutions of several systems of the first order partial differential equations (PDEs) and partial differential difference equations (PDDEs). By using the Nevanlinna theory and the Hadamard factorization theory of meromorphic functions, we establish some interesting results to describe the existence and the forms of the finite order transcendental entire solutions of the following systems of PDEs and PDDEs. Moreover, we give some examples to explain that there are significant differences in the forms of solutions from some previous systems of functional equations.

Keywords:

Nevanlinna theory, entire function, system of functional equations, several complex variables