Exact forms of entire solutions for Fermat type partial differential equations in C^2

Electronic Journal of Differential Equations

article

Yu Xian Chen¹  Hong Yan Xu² 

[1] School of Mathematics and computer science Xinyu University;School of Mathematics and computer science Xinyu University Xinyu

关键词: Fermat type;    Nevanlinna theory;    existence;    entire solution;    complex partial differential equation.;   

DOI  :  10.58997/ejde.2021.18

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

This article studies the existence and the exact form of entiresolutions of several Fermat type partial differential equations in C2,by utilizing the Nevanlinna theory of meromorphic functions in several complex variables. We obtain results about the existence and form of transcendental entire solutions with finite order for some variations of Fermat type functionalequations. Our results are extensions and generalizations of the previous theoremsby Xu and Cao [29,30], Liu and Dong [19].

【 授权许可】

CC BY