Back to Search Start Over

Results on the solutions of several second order mixed type partial differential difference equations

Results on the solutions of several second order mixed type partial differential difference equations

Authors :
Wenju Tang
Hong-Yan Xu
Keyu Zhang
Source :
AIMS Mathematics, Vol 7, Iss 2, Pp 1907-1924 (2022)
Publication Year :
2022
Publisher :
American Institute of Mathematical Sciences (AIMS), 2022.

Abstract

This article is concerned with the existence of entire solutions for the following complex second order partial differential-difference equation \begin{document}$ \left(\frac{\partial^2 f(z_1, z_2)}{\partial z_1^2}+\frac{\partial^2 f(z_1, z_2)}{\partial z_2^2}\right)^{l}+f(z_1+c_1, z_2+c_2)^{k} = 1, $\end{document} where $ c_1, c_2 $ are constants in $ \mathbb{C} $ and $ k, l $ are positive integers. In addition, we also investigate the forms of finite order transcendental entire solutions for several complex second order partial differential-difference equations of Fermat type, and obtain some theorems about the existence and the forms of solutions for the above equations. Meantime, we give some examples to explain the existence of solutions for some theorems in some cases. Our results are some generalizations of the previous theorems given by Qi [23], Xu and Cao [35], Liu, Cao and Cao [17].

Details

ISSN :
24736988
Volume :
7
Database :
OpenAIRE
Journal :
AIMS Mathematics
Accession number :
edsair.doi.dedup.....b3edc931c1a7a91fd580d3a59e168e9d
Full Text :
https://doi.org/10.3934/math.2022110