Fermat型偏微差分方程组的整函数解  

Entire Solutions of Several Fermat Type Systems of Partial Differential Difference Equations

作　　者：徐洪焱 杨连忠[2] Hong Yan XU;Lian Zhong YANG(School of Mathematics and Computer Science,Shangrao Normal University,Shangrao 334001,P.R.China;Department of Mathematics,Shandong University,Ji'nan 250100,P.R.China)

机构地区：[1]上饶师范学院数学与计算机学院,上饶334001 [2]山东大学数学学院,济南250100

出　　处：《数学学报（中文版）》2021年第6期909-932,共24页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11561033,11371225);江西省自然科学基金(20181BAB201001);江西省教育厅科技项目(GJJ190876,GJJ191042,GJJ190895)。

摘　　要：利用多变量Nevanlinna值分布理论与Nevanlinna理论的差分模拟结果,讨论了几类多变量复域Fermat型偏微差分方程组解的性质,得到了方程组有限超越整函数解的存在性条件与具体形式,推广改进了高凌云、曹廷彬、刘凯等人的结果,给出例子说明多变量与单变量方程组有限级超越整函数解之间的差异.By making use of the Nevanlinna theory and difference Nevanlinna theory of several complex variables,we investigate several Fermat type systems of partial differential difference equations,and obtain a series of results about the existence and the forms of entire solutions of such systems,which are some improvements and generalization of the previous results given by Cao,Gao,Liu et al.We also give some examples to show that there exists significant differences in the forms of transcendental entire solutions with finite order of the systems of the equations with between several complex variables and single complex variable.

关 键 词：整函数 偏微差分方程组 存在性 

分 类 号：O174[理学—数学]