On exponential dichotomy for abstract differential equations with delayed argument
UDC 517.9 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 equa...
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| Date: | 2023 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2023
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7576 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.9
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. |
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| DOI: | 10.3842/umzh.v75i8.7576 |