Application of the ergodic theory to the investigation of a boundaryvalue problem with periodic operator coefficient
We establish necessary and sufficient conditions for the solvability of a family of differential equations with periodic operator coefficient and periodic boundary condition by using the notion of the relative spectrum of a linear bounded operator in a Banach space and the ergodic theorem. We show...
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| Date: | 2013 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2013
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2422 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We establish necessary and sufficient conditions for the solvability of a family of differential equations with periodic operator coefficient and periodic boundary condition by
using the notion of the relative spectrum of a linear bounded operator in a Banach space and the ergodic theorem.
We show that if the existence condition is satisfied, then these periodic solutions can be constructed by using the formula
for the generalized inverse of a linear bounded operator obtained in the present paper. |
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