非线性微分方程的Hyers-Ulam稳定性  

Hyers-Ulam stability of nonlinear differential equations

作　　者：黎永锦[1] 华柳斌[2] 

机构地区：[1]中山大学数学系,广东广州510275 [2]广州松田职业学院,广东广州511370

出　　处：《暨南大学学报（自然科学与医学版）》2013年第5期464-466,共3页Journal of Jinan University(Natural Science & Medicine Edition)

基　　金：国家自然科学基金资助项目(10871213)

摘　　要：证明了非线性微分方程yy'=1在边界条件y(a)=1下具有Hyers-Ulam稳定性,即存在常数k>0,使得对于任意ε>0,y∈C1[a,b],若|yy'-1|≤ε,y(a)=1,则存在z∈C1[a,b]满足zz'-1=0且z(a)=1,使得|y(x)-z(x)|<Kε.The Hyers-Ulam stability of nonlinear differential equations yy＇ = 1 with initial conditions y（a）=1 was proved. It means there exists k 〉0, such that for any ε〉0,Y∈C1[0,b],whenever 1yy＇-1｜≤ε,then there exists z∈C1[a,b] with zz＇=1=0and z（a）=1,such that ｜y（x）-z（x）｜〈Kε

关 键 词：HYERS-ULAM稳定性 非线性微分方程 边界条件 

分 类 号：O177.2[理学—数学]