SOME RESULTS REGARDING PARTIAL DIFFERENTIAL POLYNOMIALS AND THE UNIQUENESS OF MEROMORPHIC FUNCTIONS IN SEVERAL VARIABLES  

作　　者：刘曼莉 高凌云 房少梅 Manli LIU;Lingyun GAO;Shaomei FANG(Department of Mathematics,South China Agricultural University,Guangzhou 510642,China;Department of Mathematics,Jinan University,Guangzhou 510632,China)

机构地区：[1]Department of Mathematics,South China Agricultural University,Guangzhou 510642,China [2]Department of Mathematics,Jinan University,Guangzhou 510632,China

出　　处：《Acta Mathematica Scientia》2023年第2期821-838,共18页数学物理学报（B辑英文版）

基　　金：partially supported by the NSFC(11271227,11271161);the PCSIRT(IRT1264);the Fundamental Research Funds of Shandong University(2017JC019)。

摘　　要：In this paper,we mainly investigate the value distribution of meromorphic functions in Cmwith its partial differential and uniqueness problem on meromorphic functions in Cmand with its k-th total derivative sharing small functions.As an application of the value distribution result,we study the defect relation of a nonconstant solution to the partial differential equation.In particular,we give a connection between the Picard type theorem of Milliox-Hayman and the characterization of entire solutions of a partial differential equation.

关 键 词：meromorphic function in several variables Nevanlinna theory partial differ-ential equation total derivative 

分 类 号：O174.14[理学—数学] O174.52[理学—基础数学]