It is known that hyperbolic nonautonomous 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.
CITATION STYLE
Backes, L., Dragičević, D., & Pituk, M. (2024). Shadowing, Hyers-Ulam stability and hyperbolicity for nonautonomous linear delay differential equations. Communications in Contemporary Mathematics. https://doi.org/10.1142/S0219199724500123
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