Upper and lower absolutely continuous functions with applications to discontinuous differential equations
We use upper and lower absolutely continuous functions as subsolutions and supersolutions to discontinuous ordinary differential equations. We present sufficient conditions for the existence of extremal solutions to initial value problems. Due to a new notion of sub and supersolutions we generaliz...
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| Format: | Article |
| Language: | English |
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University of Szeged
2017-11-01
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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=6075 |
| _version_ | 1797830563681271808 |
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| author | Krzysztof Topolski |
| author_facet | Krzysztof Topolski |
| author_sort | Krzysztof Topolski |
| collection | DOAJ |
| description | We use upper and lower absolutely continuous functions as subsolutions and supersolutions to discontinuous ordinary differential equations. We present sufficient conditions for the existence of extremal solutions to initial value problems. Due to a new notion of sub and supersolutions we generalize previous results and present elementary and relatively simple proofs. |
| first_indexed | 2024-04-09T13:38:05Z |
| format | Article |
| id | doaj.art-2e384a8e017b41dd9467696bbef77bd9 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:05Z |
| publishDate | 2017-11-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-2e384a8e017b41dd9467696bbef77bd92023-05-09T07:53:07ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752017-11-0120178311210.14232/ejqtde.2017.1.836075Upper and lower absolutely continuous functions with applications to discontinuous differential equationsKrzysztof Topolski0Institute of Mathematics, University of Gdansk, Gdansk, PolandWe use upper and lower absolutely continuous functions as subsolutions and supersolutions to discontinuous ordinary differential equations. We present sufficient conditions for the existence of extremal solutions to initial value problems. Due to a new notion of sub and supersolutions we generalize previous results and present elementary and relatively simple proofs.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6075generalized solutiondiscontinuous differential equations |
| spellingShingle | Krzysztof Topolski Upper and lower absolutely continuous functions with applications to discontinuous differential equations Electronic Journal of Qualitative Theory of Differential Equations generalized solution discontinuous differential equations |
| title | Upper and lower absolutely continuous functions with applications to discontinuous differential equations |
| title_full | Upper and lower absolutely continuous functions with applications to discontinuous differential equations |
| title_fullStr | Upper and lower absolutely continuous functions with applications to discontinuous differential equations |
| title_full_unstemmed | Upper and lower absolutely continuous functions with applications to discontinuous differential equations |
| title_short | Upper and lower absolutely continuous functions with applications to discontinuous differential equations |
| title_sort | upper and lower absolutely continuous functions with applications to discontinuous differential equations |
| topic | generalized solution discontinuous differential equations |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6075 |
| work_keys_str_mv | AT krzysztoftopolski upperandlowerabsolutelycontinuousfunctionswithapplicationstodiscontinuousdifferentialequations |