Robustness of Hyperbolicity in Delay Equations
- 9 Downloads
We establish the robustness of the notion of an exponential dichotomy for a nonautonomous linear delay equation. We consider the general cases of equations satisfying the Carathéodory conditions and of noninvertible evolution families defined by the linear equations. The stable and unstable spaces of the perturbed equations are obtained as images of linear operators that in their turn are fixed points of appropriate contraction maps.
KeywordsDelay equations Exponential dichotomies Robustness
Mathematics Subject ClassificationPrimary 34K06 37D99
- 4.Dalec’kiĭ, J.u., Kreĭn, M.: Stability of Solutions of Differential Equations in Banach space, Translations of Mathematical Monographs, vol. 43. American Mathematical Society, Providence, RI (1974)Google Scholar