Continuity in a parameter of solutions to boundary-value problems in Sobolev spaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866908720245506048 |
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| author | Atlasiuk, Olena Mikhailets, Vladimir |
| author_facet | Atlasiuk, Olena Mikhailets, Vladimir |
| contents | We consider the most general class of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of an arbitrary order whose solutions and right-hand sides belong to appropriate Sobolev spaces. For parameter-dependent problems from this class, we prove a constructive criterion for their solutions to be continuous in the Sobolev space with respect to the parameter. We also prove a two-sided estimate for the degree of convergence of these solutions to the solution of the nonperturbed problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_03494 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Continuity in a parameter of solutions to boundary-value problems in Sobolev spaces Atlasiuk, Olena Mikhailets, Vladimir Classical Analysis and ODEs 34B08 We consider the most general class of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of an arbitrary order whose solutions and right-hand sides belong to appropriate Sobolev spaces. For parameter-dependent problems from this class, we prove a constructive criterion for their solutions to be continuous in the Sobolev space with respect to the parameter. We also prove a two-sided estimate for the degree of convergence of these solutions to the solution of the nonperturbed problem. |
| title | Continuity in a parameter of solutions to boundary-value problems in Sobolev spaces |
| topic | Classical Analysis and ODEs 34B08 |
| url | https://arxiv.org/abs/2005.03494 |