Electron. J. Differential Equations, Vol. 2024 (2024), No. 61, pp. 1-15.

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

Abhijit Banerjee, Jhuma Sarkar

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.
DOI: 10.58997/ejde.2024.61

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Abhijit Banerjee
Department of Mathematics
University of Kalyani
West Bengal 741235, India
email: abanerjee_kal@yahoo.co.in
Jhuma Sarkar
Department of Mathematics
University of Kalyani
West Bengal 741235, India
email: jhumasarkar928@gmail.com

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