非线性微分方程的Hyers-Ulam稳定性

Hyers-Ulam stability of nonlinear differential equations

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