On solvability of focal boundary value problems for higher order functional differential equations with integral restrictions
Sharp conditions are obtained for the unique solvability of focal boundary value problems for higher-order functional differential equations under integral restrictions on functional operators. In terms of the norm of the functional operator, unimprovable conditions for the unique solvability of the...
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| Format: | Article |
| Language: | English |
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University of Szeged
2021-03-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8778 |
| _version_ | 1827951077827280896 |
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| author | Eugene Bravyi |
| author_facet | Eugene Bravyi |
| author_sort | Eugene Bravyi |
| collection | DOAJ |
| description | Sharp conditions are obtained for the unique solvability of focal boundary value problems for higher-order functional differential equations under integral restrictions on functional operators. In terms of the norm of the functional operator, unimprovable conditions for the unique solvability of the boundary value problem are established in the explicit form. If these conditions are not fulfilled, then there exists a positive bounded operator with a given norm such that the focal boundary value problem with this operator is not uniquely solvable. In the symmetric case, some estimates of the best constants in the solvability conditions are given. Comparison with existing results is also performed. |
| first_indexed | 2024-04-09T13:37:07Z |
| format | Article |
| id | doaj.art-43c71b6579014c9e9e0485af49cb95e5 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:07Z |
| publishDate | 2021-03-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-43c71b6579014c9e9e0485af49cb95e52023-05-09T07:53:11ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752021-03-0120212211410.14232/ejqtde.2021.1.228778On solvability of focal boundary value problems for higher order functional differential equations with integral restrictionsEugene Bravyi0Perm National Research Polytechnic University, Perm, RussiaSharp conditions are obtained for the unique solvability of focal boundary value problems for higher-order functional differential equations under integral restrictions on functional operators. In terms of the norm of the functional operator, unimprovable conditions for the unique solvability of the boundary value problem are established in the explicit form. If these conditions are not fulfilled, then there exists a positive bounded operator with a given norm such that the focal boundary value problem with this operator is not uniquely solvable. In the symmetric case, some estimates of the best constants in the solvability conditions are given. Comparison with existing results is also performed.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8778functional differential equationsfocal boundary value problemunique solvability |
| spellingShingle | Eugene Bravyi On solvability of focal boundary value problems for higher order functional differential equations with integral restrictions Electronic Journal of Qualitative Theory of Differential Equations functional differential equations focal boundary value problem unique solvability |
| title | On solvability of focal boundary value problems for higher order functional differential equations with integral restrictions |
| title_full | On solvability of focal boundary value problems for higher order functional differential equations with integral restrictions |
| title_fullStr | On solvability of focal boundary value problems for higher order functional differential equations with integral restrictions |
| title_full_unstemmed | On solvability of focal boundary value problems for higher order functional differential equations with integral restrictions |
| title_short | On solvability of focal boundary value problems for higher order functional differential equations with integral restrictions |
| title_sort | on solvability of focal boundary value problems for higher order functional differential equations with integral restrictions |
| topic | functional differential equations focal boundary value problem unique solvability |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8778 |
| work_keys_str_mv | AT eugenebravyi onsolvabilityoffocalboundaryvalueproblemsforhigherorderfunctionaldifferentialequationswithintegralrestrictions |