摘要
文章利用多变量Nevanlinna理论与偏微分方程的特征方程讨论了C^(2)内一阶复域偏微分方程(au+bu_(z1))(cu+du_(z1))=1与(au+bu_(z1))(cu+du_(z2))=1的超越整函数解,这里a,b,c,d为复常数,u_(z1)=δu/δ_(z1),u_(z2)=δu/δ_(z2),获得了方程具有有限级超越整函数解的存在性条件及其形式等结果,推广改进了前人的结果。
This article utilized the Nevanlinna theory with several complex variables and the Characteristic equation of partial differential equation to investigate the solutions to several firstorder complex partial differential equations of the forms(au+bu_(z1))(cu+du_(z1))=1and(au+bu_(z1))(cu+du_(z2))=1in C^(2),where a,b,c,d are complex numbers,u_(z1)=δu/δ_(z1)and u_(z2)=δu/δ_(z2).Some theorems about the existence and the forms of the finite order transcendental entire solutions to such equations were obtained,generalizing and improving some the previous theorems.
作者
徐士权
刘晓兰
徐洪焱
XU Shiquan;LIU Xiaolan;XU Hongyan(Suqian Middle School of Jiangsu Province;College of Arts and Sciences,Suqian University,Suqian,Jiangsu 223800,China)
出处
《南昌大学学报(理科版)》
CAS
北大核心
2023年第5期421-425,共5页
Journal of Nanchang University(Natural Science)
基金
国家自然科学基金项目(12161074)
宿迁学院科研启动金项目(106-CK00042/028)。
关键词
NEVANLINNA理论
偏微分方程
超越
整函数
Nevanlinna theory
the partial differential equation
transcendental
entire function