Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 61, pp. 1-15.

Title: Existence and forms of entire solutions to system  of non-linear partial differential equations

Authors: Abhijit Banerjee (Univ. of Kalyani, West Bengal, India)
         Jhuma Sarkar (Univ. of Kalyani, West Bengal, India)

Abstract: 
The main objective of this article is to explore the existence and forms
of transcendental entire solutions of some systems of non-linear 
partial differential equations. 
We obtain two results and illustrate the results with several 
examples. This article improves the results in [5,15].
In the last section we discuss the differences between the solutions involving
homogeneous and non-homogeneous operators, 
and state an open question for the sake of future research.

Submitted June 12, 2024. Published October 15, 2024.
Math Subject Classifications: 32H30, 35M30.
Key Words: Fermat-type equation; transcendental entire solution; partial differential operator.