Differential systems in Sobolev spaces with generic inhomogeneous boundary conditions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909400990482432 |
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| author | Mikhailets, Vladimir Atlasiuk, Olena |
| author_facet | Mikhailets, Vladimir Atlasiuk, Olena |
| contents | The paper contains a review of results on linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general inhomogeneous boundary conditions in Sobolev spaces. The character of the solvability of such problems is investigated, their Fredholm properties are established, and their indexes and the dimensions of their kernels and co-kernels are found. In addition, necessary and sufficient conditions of continuity in the parameter of the solutions of the introduced classes of boundary-value problems in Sobolev spaces of an arbitrary order are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15330 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differential systems in Sobolev spaces with generic inhomogeneous boundary conditions Mikhailets, Vladimir Atlasiuk, Olena Classical Analysis and ODEs Analysis of PDEs 34B05, 34B08, 34B10, 47A53 The paper contains a review of results on linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general inhomogeneous boundary conditions in Sobolev spaces. The character of the solvability of such problems is investigated, their Fredholm properties are established, and their indexes and the dimensions of their kernels and co-kernels are found. In addition, necessary and sufficient conditions of continuity in the parameter of the solutions of the introduced classes of boundary-value problems in Sobolev spaces of an arbitrary order are obtained. |
| title | Differential systems in Sobolev spaces with generic inhomogeneous boundary conditions |
| topic | Classical Analysis and ODEs Analysis of PDEs 34B05, 34B08, 34B10, 47A53 |
| url | https://arxiv.org/abs/2411.15330 |