Second order tangency conditions and differential inclusions: a counterexample and a remedy
In this paper we show that second order tangency conditions are superfluous not to say useless while discussing the existence condition for certain second order differential inclusions. In this regard, a counterexample is provided even in the simpler setting of second order differential equation...
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| Format: | Article |
| Language: | English |
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Texas State University
2009-01-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2009/23/abstr.html |
| _version_ | 1818407146694377472 |
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| author | Corneliu Ursescu |
| author_facet | Corneliu Ursescu |
| author_sort | Corneliu Ursescu |
| collection | DOAJ |
| description | In this paper we show that second order tangency conditions are superfluous not to say useless while discussing the existence condition for certain second order differential inclusions. In this regard, a counterexample is provided even in the simpler setting of second order differential equations, where a substitute condition is propound. In the setting of differential inclusions, the corresponding substitute condition allows for us to prove existence of sufficiently many approximate solutions without the use of any convexity, measurability, or upper semicontinuity assumption. Accordingly, some proofs in the related literature are greatly simplified. |
| first_indexed | 2024-12-14T09:23:12Z |
| format | Article |
| id | doaj.art-84dcb1b1cfaa465b9181233771bde594 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-14T09:23:12Z |
| publishDate | 2009-01-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-84dcb1b1cfaa465b9181233771bde5942022-12-21T23:08:15ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912009-01-01200923,117Second order tangency conditions and differential inclusions: a counterexample and a remedyCorneliu UrsescuIn this paper we show that second order tangency conditions are superfluous not to say useless while discussing the existence condition for certain second order differential inclusions. In this regard, a counterexample is provided even in the simpler setting of second order differential equations, where a substitute condition is propound. In the setting of differential inclusions, the corresponding substitute condition allows for us to prove existence of sufficiently many approximate solutions without the use of any convexity, measurability, or upper semicontinuity assumption. Accordingly, some proofs in the related literature are greatly simplified.http://ejde.math.txstate.edu/Volumes/2009/23/abstr.htmlSecond order differential inclusionssecond order tangency inclusions |
| spellingShingle | Corneliu Ursescu Second order tangency conditions and differential inclusions: a counterexample and a remedy Electronic Journal of Differential Equations Second order differential inclusions second order tangency inclusions |
| title | Second order tangency conditions and differential inclusions: a counterexample and a remedy |
| title_full | Second order tangency conditions and differential inclusions: a counterexample and a remedy |
| title_fullStr | Second order tangency conditions and differential inclusions: a counterexample and a remedy |
| title_full_unstemmed | Second order tangency conditions and differential inclusions: a counterexample and a remedy |
| title_short | Second order tangency conditions and differential inclusions: a counterexample and a remedy |
| title_sort | second order tangency conditions and differential inclusions a counterexample and a remedy |
| topic | Second order differential inclusions second order tangency inclusions |
| url | http://ejde.math.txstate.edu/Volumes/2009/23/abstr.html |
| work_keys_str_mv | AT corneliuursescu secondordertangencyconditionsanddifferentialinclusionsacounterexampleandaremedy |