文献类型：期刊文献

英文题名：Results on solutions of several product type nonlinear partial differential equations in C3

作者：Xu H.Y.; Liu K.; Xuan Z.

机构：[1]School of Arts and Sciences, Suqian University, Jiangsu, Suqian, 223800, China;[2]School of Mathematics and Computer Science, Shangrao Normal University, Jiangxi, Shangrao, 334001, China;[3]Department of Mathematics, Nanchang University, Jiangxi, Nanchang, 330031, China;[4]Department of General Education, Beijing Union University, No.97 Bei Si Huan Dong Road, Beijing, 100101, Chaoyang District, China

第一机构：School of Arts and Sciences, Suqian University, Jiangsu, Suqian, 223800, China

年份：2025

卷号：543

期号：1

外文期刊名：Journal of Mathematical Analysis and Applications

收录：Scopus(收录号：2-s2.0-85204475179)

语种：英文

外文关键词：Entire solution; Nevanlinna theory; Partial differential equation

摘要：This paper is devoted to exploring the solutions of the product type nonlinear partial differential equations (PDEs) with three complex variables. By making use of Nevanlinna theory with several complex variables and Hadamard factorization theory of meromorphic functions, and combining with the properties of the full rank determinants and algebraic cofactor, we prove that equation ∏i=13(ai1uz+ai2uz+ai3uz)=1 in C3 has no any finite order transcendental entire solution under the condition that the rank of the following matrix A=(a11a12a13a21a22a23a31a32a33) is full rank, i.e. R(A)=3, where aij(i,j=1,2,3) are constants in C. Our results are some improvements and generalizations of the previous results given by Saleeby, Li, Lü and Xu. Meantime, we list some examples to explain that the condition in our theorem can not be removed. ? 2024 Elsevier Inc.