On the Hyers-Ulam stability of the Banach space-valued differential equation \(y'=\lambda y\). (English) Zbl 1011.34046

Takahasi, Sin-Ei; Miura, Takeshi; Miyajima, Shizuo

Bull. Korean Math. Soc. 39, No. 2, 309-315 (2002).

The Hyers-Ulam stability is analyzed for the differential equation \(y'=\lambda y\), where \(y\) maps an open interval of \(\mathbb{R}\) into a complex Banach space. The authors prove a sufficient condition that allows one to estimate the distance between some given function \(\varphi\) and the set of all solutions to the differential equation above.

Reviewer: Etienne Emmrich (Berlin)

MSC:

34D30	Structural stability and analogous concepts of solutions to ordinary differential equations
34G10	Linear differential equations in abstract spaces
26D10	Inequalities involving derivatives and differential and integral operators

Keywords:

Banach space; ordinary differential equation; exponential function; Hyers-Ulam stability