Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 37, pp. 1-15.

Title: Forms of entire solutions of partial differential difference equations with constant coefficients

Authors: Xin Ding (Jiangxi Normal Univ., Nanchang, China)
         Xiu Min Zheng (Jiangxi Normal Univ., Nanchang, China)

Abstract: 
The purpose of this article is to describe the transcendental entire solutions of 
quadratic trinomial partial differential equations (PDDEs) with constant coefficients. 
We establish  theorems on the forms of finite order transcendental entire 
solutions for such PDDEs, which generalize and improve previous theorems. 
Some examples confirm the existence and the forms of transcendental entire 
solutions with finite order of such equations.

Submitted April 30, 2024. Published June 22, 2024.
Math Subject Classifications: 30D35, 39A13.
Key Words: Nevanlinna theory; entire solution; existence.