两类非线性微分—差分方程的整函数解  

Entire solutions of two types of nonlinear differential-difference equations

作　　者：高真光 GAO Zhen-guang(College of Information Science and Technology,Jinan University,Guangzhou 510632,Guangdong,China)

机构地区：[1]暨南大学信息科学技术学院,广东广州510632

出　　处：《山东大学学报（理学版）》2022年第12期34-44,共11页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12171127)。

摘　　要：利用Nevanlinna值分布理论,研究了两类非线性微分-差分方程f^(n)+ωf^(n-1)f′+b(f′)^(n)+qe^(Q)f(z+c)=uev和f^(n)+ω_(1)f^(n-1)f′+ω_(2)(f′)^(n)+qe^(Q)f(z+c)=p_(1)e^(λ)_(1)^(z)+p_(2)e^(λ)_(2)^(z)的有限级整函数解的存在性,得到了两个结果,并举例证明文中所得结果是精确的。Using Nevanlinna′s value distribution theory, this paper investigates the existence of entire solutions with finite order of two types of nonlinear differential-difference equations of the forms f^(n)+ωf^(n-1)f ′+b(f ′)^(n)+qe^(Q)f(z+c)=uevand f^(n)+ω_(1)f^(n-1)f ′+ω_(2)(f ′)^(n)+qe^(Q)f(z+c)=p_(1)e^(λ)_(1)^(z)+p_(2)e^(λ)_(2)^(z), and obtains two results. Examples are provided to show that the results obtained in this paper, in a sense, are best possible.

关 键 词：非线性微分-差分方程 整函数解 主次项 增长级 

分 类 号：O174.52[理学—数学] O175.7[理学—基础数学]