Shadowing, Hyers--Ulam stability and hyperbolicity for nonautonomous linear delay differential equations

Abstract

It is known that hyperbolic non\-autonomous linear delay differential equations in a finite dimensional space are Hyers--Ulam stable and hence shadowable. The converse result is available only in the special case of autonomous and periodic linear delay differential equations with a simple spectrum. In this paper, we prove the converse and hence the equivalence of all three notions in the title for a general class of nonautonomous linear delay differential equations with uniformly bounded coefficients. The importance of the boundedness assumption is shown by an example.

References in corpus (1)

• Shadowing for infinite dimensional dynamics and exponential trichotomies

Cited by in corpus (1)

• Shadowing and hyperbolicity for linear delay difference equations