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https://er.knutd.edu.ua/handle/123456789/25233
Title: | On exponential dichotomy for abstract differential equations with delayed argument |
Other Titles: | Про експоненціальну дихотомію для абстрактних диференціальних рівнянь з запізненням аргументу |
Authors: | Chaikovs'kyi, Andrii Lagoda, Oksana |
Keywords: | differential equations with delayed arguments in a Banach space the condition of exponential dichotomy |
Issue Date: | 30-Aug-2023 |
Citation: | Chaikovs'kyi A. On exponential dichotomy for abstract differential equations with delayed argument / A. Chaikovs'kyi, O. Lagoda // Ukrains’kyi Matematychnyi Zhurnal. – 2023. – Vol. 75, № 8, August. – Р. 1-11. – Режим доступу: https://umj.imath.kiev.ua/index.php/umj/article/view/7576 |
Source: | Ukrains’kyi Matematychnyi Zhurnal |
Abstract: | We consider linear differential equations of the first order with delayed arguments in a Banach space. We establish conditions for the operator coefficients necessary for the existence of exponential dichotomy on the real axis. It is proved that the analyzed differential equation is equivalent to a difference equation in a certain space. It is shown that, under the conditions of existence and uniqueness of a solution bounded on the entire real axis, the condition of exponential dichotomy is also satisfied for any bounded known function. The explicit formula for projectors, which form the dichotomy, is found for the case of a single delay. |
URI: | https://er.knutd.edu.ua/handle/123456789/25233 |
Faculty: | Інститут інженерії та інформаційних технологій |
Department: | Кафедра прикладної фізики та вищої математики |
ISSN: | 0041-6053 (print) 1027-3190 (online) |
Appears in Collections: | Наукові публікації (статті) Кафедра прикладної фізики та вищої математики (ПФВМ) |
Files in This Item:
File | Description | Size | Format | |
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11-Chaikovskyi.pdf | Chaikovs’kyi, A., and O. Lagoda. “On Exponential Dichotomy for Abstract Differential Equations With Delayed Argument” | 182,07 kB | Adobe PDF | View/Open |
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