Solvability of linear boundary-value problems for ordinary differential systems in the space $C^{n}$
UDC 517.927 We study linear boundary-value problems for systems of first-order ordinary differential equations with the most general boundary conditions in the normed spaces of continuously differentiable functions on a finite closed interval. The boundary conditions are allowed to be overdetermined...
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| Date: | 2025 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2025
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8940 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.927
We study linear boundary-value problems for systems of first-order ordinary differential equations with the most general boundary conditions in the normed spaces of continuously differentiable functions on a finite closed interval. The boundary conditions are allowed to be overdetermined or underdetermined with respect to the differential system and may contain arbitrary derivatives of the unknown functions. We prove that the problem operator is Fredholm on appropriate pairs of normed spaces, find its index and $d$-characteristics, and prove the limit theorems for sequences of characteristic matrices of the investigated boundary-value problems and $d$-characteristics of the corresponding Fredholm operators. |
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| DOI: | 10.3842/umzh.v77i3.8940 |