Please use this identifier to cite or link to this item: 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)

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