Electron. J. Differential Equations, Vol. 2024 (2024), No. 37, pp. 1-15.

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

Xin Ding, Xiu Min Zheng

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.
DOI: 10.58997/ejde.2024.37

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Xin Ding
School of Mathematics and Statistics
Jiangxi Normal University
Nanchang, 330022, China.
email: dingxin2001@126.com
Xiu Min Zheng
School of Mathematics and Statistics
Jiangxi Normal University
Nanchang, 330022, China
email: zhengxiumin2008@sina.com

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