一类非线性差分方程亚纯解的增长性  

The Growth of Meromorphic Solutions of Some Type of Nonlinear Difference Equations

作　　者：钟进凤 刘慧芳[1] ZHONG Jinfeng;LIU Huifang(College of Mathematics and Informatics,Jiangxi Normal University,Nanchang Jiangxi 330022,China)

机构地区：[1]江西师范大学数学与信息科学学院

出　　处：《江西师范大学学报（自然科学版）》2019年第5期508-512,共5页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11661044)资助项目

摘　　要：应用Nevanlinna理论研究非线性差分方程f^n(z)+P d(z,f)=p 1^e^α1(z)+p 2^e^α2(z)亚纯解的存在性,其中P d(z,f)为f的d次差分多项式,p 1,p 2为f的非零小函数,α1,α2为级小于1的非常数整函数,得到上述方程存在超级小于1的亚纯解的必要条件和解的表达式.Using Nevanlinna theory,the existence of meromorphic solutions of the nonlinear difference equation f^n(z)+P d(z,f)=p 1^e^α1(z)+p 2^e^α2(z)are investigated,where P d(z,f)is a difference polynomial in f of degree d,p 1,p 2 are non-vanishing small meromorphic functions of f,andα1,α2 are non-constant entire functions with order less than 1.Some necessary conditions that guarantee the above equation admits meromorphic solutions of hyper-order less than 1 and the expression for the solution are obtained.

关 键 词：差分方程 亚纯函数 增长级 

分 类 号：O174.52[理学—数学]