几类一阶复域偏微分方程的超越整函数解

Transcendental entire solutions of several first order complex partial differential equations

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.