Admissibility and general dichotomies for evolution families
For an arbitrary noninvertible evolution family on the half-line and for ρ : [0, ∞) → [0, ∞) in a large class of rate functions, we consider the notion of a ρdichotomy with respect to a family of norms and characterize it in terms of two admissibility conditions. In particular, our results are appli...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2020
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciálegyenlet |
| doi: | 10.14232/ejqtde.2020.1.58 |
| Online Access: | http://acta.bibl.u-szeged.hu/70942 |
| Tartalmi kivonat: | For an arbitrary noninvertible evolution family on the half-line and for ρ : [0, ∞) → [0, ∞) in a large class of rate functions, we consider the notion of a ρdichotomy with respect to a family of norms and characterize it in terms of two admissibility conditions. In particular, our results are applicable to exponential as well as polynomial dichotomies with respect to a family of norms. As a nontrivial application of our work, we establish the robustness of general nonuniform dichotomies. |
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| ISSN: | 1417-3875 |