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arXiv · 1907.02515

Admissibility and polynomial dichotomies for evolution families

Davor Dragicevic
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Abstract

For an arbitrary evolution family, we consider the notion of a polynomial dichotomy with respect to a family of norms and characterize it in terms of the admissibility property, that is, the existence of a unique bounded solution for each bounded perturbation. In particular, by considering a family of Lyapunov norms, we recover the notion of a (strong) nonuniform polynomial dichotomy. As a nontrivial application of the characterization, we establish the robustness of the notion of a strong nonuniform polynomial dichotomy under sufficiently small linear perturbations.

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Davor Dragicevic. 2019-07-02. Admissibility and polynomial dichotomies for evolution families. https://arxiv.org/abs/1907.02515

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