Admissibility and general dichotomies for evolution families
For an arbitrary noninvertible evolution family on the half-line and for $\rho \colon [0, \infty)\to [0, \infty)$ in a large class of rate functions, we consider the notion of a $\rho$-dichotomy with respect to a family of norms and characterize it in terms of two admissibility conditions. In parti...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2020-10-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8307 |
| _version_ | 1797830513186045952 |
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| author | Davor Dragičević Nevena Jurčević Peček Nicolae Lupa |
| author_facet | Davor Dragičević Nevena Jurčević Peček Nicolae Lupa |
| author_sort | Davor Dragičević |
| collection | DOAJ |
| description | For an arbitrary noninvertible evolution family on the half-line and for $\rho \colon [0, \infty)\to [0, \infty)$ in a large class of rate functions, we consider the notion of a $\rho$-dichotomy 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. |
| first_indexed | 2024-04-09T13:37:18Z |
| format | Article |
| id | doaj.art-6ec59144e5bc4c79a0398510079211d4 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:18Z |
| publishDate | 2020-10-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-6ec59144e5bc4c79a0398510079211d42023-05-09T07:53:10ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752020-10-0120205811910.14232/ejqtde.2020.1.588307Admissibility and general dichotomies for evolution familiesDavor Dragičević0Nevena Jurčević Peček1Nicolae Lupa2Department of Mathematics, University of Rijeka, CroatiaDepartment of Mathematics, University of Rijeka, CroatiaDepartment of Mathematics, Politehnica University of Timisoara, RomaniaFor an arbitrary noninvertible evolution family on the half-line and for $\rho \colon [0, \infty)\to [0, \infty)$ in a large class of rate functions, we consider the notion of a $\rho$-dichotomy 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.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8307admissibilitydichotomies with growth ratesrobustness |
| spellingShingle | Davor Dragičević Nevena Jurčević Peček Nicolae Lupa Admissibility and general dichotomies for evolution families Electronic Journal of Qualitative Theory of Differential Equations admissibility dichotomies with growth rates robustness |
| title | Admissibility and general dichotomies for evolution families |
| title_full | Admissibility and general dichotomies for evolution families |
| title_fullStr | Admissibility and general dichotomies for evolution families |
| title_full_unstemmed | Admissibility and general dichotomies for evolution families |
| title_short | Admissibility and general dichotomies for evolution families |
| title_sort | admissibility and general dichotomies for evolution families |
| topic | admissibility dichotomies with growth rates robustness |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8307 |
| work_keys_str_mv | AT davordragicevic admissibilityandgeneraldichotomiesforevolutionfamilies AT nevenajurcevicpecek admissibilityandgeneraldichotomiesforevolutionfamilies AT nicolaelupa admissibilityandgeneraldichotomiesforevolutionfamilies |