复域偏微分方程(组)超越整函数解的存在性

The Existence of Finite Order Transcendental Entire Solutions of Complex Partial Differential Equation (System)

文章通过多变量值分布理论研究复偏微分方程与方程组的解,得到一类偏微分方程与一类偏微分方程组有限级超越整函数解的存在性及其形式.同时,我们举例说明了结果是精确的.

By making use of the Nevanlinna theory in several complex variables,we investigate the entire solutions of a class of complex partial differential equation and a system of complex partial differential equations,and obtain some theorems involving the existence and the forms of several complex partial differential equations and complex partial differential equations system of Fermat type.Meantime,we give some examples to show that our results are precise.