The study of solutions for several systems of PDDEs with two complex variables

Abstract

The purpose of this article is to describe the properties of the pair of solutions of several systems of Fermat-type partial differential difference equations. Our theorems exhibit the forms of finite order transcendental entire solutions for these systems, which are some extensions and improvement of the previous theorems given by Xu, Cao, Liu, etc. Furthermore, we give a series of examples to show that the existence conditions and the forms of transcendental entire solutions with finite order of such systems are precise.

Keywords

• partial differential difference equation
• entire solution
• nevanlinna theory
• 30d 35
• 35m 30
• 39a 45