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
出处
《暨南大学学报(自然科学与医学版)》
CAS
CSCD
北大核心
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)