Optimal control and approximate controllability for second-order integro-differential equations with state-dependent delay and non-instantaneous impulses
This article concerns the optimal control and the approximate controllability for second order integro-differential equation with state-dependent delay and non-instantaneous impulses. We first establish the existence of mild solution for the control system. Then, based on these results, we invest...
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| Format: | Article |
| Language: | English |
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Texas State University
2025-05-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2025/54/abstr.html |
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| author | Abdelhamid Bensalem Abdelkrim Salim Mouffak Benchohra Gaston M. N'Guerekata |
| author_facet | Abdelhamid Bensalem Abdelkrim Salim Mouffak Benchohra Gaston M. N'Guerekata |
| author_sort | Abdelhamid Bensalem |
| collection | DOAJ |
| description | This article concerns the optimal control and the approximate controllability
for second order integro-differential equation with state-dependent delay
and non-instantaneous impulses. We first
establish the existence of mild solution for the control system.
Then, based on these results, we investigate the approximate controllability
and show the existence of optimal controls for Bolza problems by using the
resolvent family of linear operators, M\"{o}nch's fixed point theorem, and
the resolvent condition. Finally, we give an example to illustrate the
effectiveness of the results. |
| format | Article |
| id | doaj-art-7ca6e247439947ec886a4a8b60d090db |
| institution | Kabale University |
| issn | 1072-6691 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj-art-7ca6e247439947ec886a4a8b60d090db2025-08-20T04:02:45ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912025-05-01202554,118Optimal control and approximate controllability for second-order integro-differential equations with state-dependent delay and non-instantaneous impulsesAbdelhamid Bensalem0Abdelkrim Salim1Mouffak Benchohra2Gaston M. N'Guerekata3 Djillali Liabes Univ. of Sidi Bel-Abbes, Algeria Djillali Liabes Univ. of Sidi Bel-Abbes, Algeria Djillali Liabes Univ. of Sidi Bel-Abbes, Algeria Morgan State Univ., Baltimore, MD, USA This article concerns the optimal control and the approximate controllability for second order integro-differential equation with state-dependent delay and non-instantaneous impulses. We first establish the existence of mild solution for the control system. Then, based on these results, we investigate the approximate controllability and show the existence of optimal controls for Bolza problems by using the resolvent family of linear operators, M\"{o}nch's fixed point theorem, and the resolvent condition. Finally, we give an example to illustrate the effectiveness of the results.http://ejde.math.txstate.edu/Volumes/2025/54/abstr.htmlapproximate controllabilityoptimal controlfixed point theoreminfinite delaysecond-order integrodifferential equationimpulsivemeasures of noncompactnessmild solutionresolvent operator |
| spellingShingle | Abdelhamid Bensalem Abdelkrim Salim Mouffak Benchohra Gaston M. N'Guerekata Optimal control and approximate controllability for second-order integro-differential equations with state-dependent delay and non-instantaneous impulses Electronic Journal of Differential Equations approximate controllability optimal control fixed point theorem infinite delay second-order integrodifferential equation impulsive measures of noncompactness mild solution resolvent operator |
| title | Optimal control and approximate controllability for second-order integro-differential equations with state-dependent delay and non-instantaneous impulses |
| title_full | Optimal control and approximate controllability for second-order integro-differential equations with state-dependent delay and non-instantaneous impulses |
| title_fullStr | Optimal control and approximate controllability for second-order integro-differential equations with state-dependent delay and non-instantaneous impulses |
| title_full_unstemmed | Optimal control and approximate controllability for second-order integro-differential equations with state-dependent delay and non-instantaneous impulses |
| title_short | Optimal control and approximate controllability for second-order integro-differential equations with state-dependent delay and non-instantaneous impulses |
| title_sort | optimal control and approximate controllability for second order integro differential equations with state dependent delay and non instantaneous impulses |
| topic | approximate controllability optimal control fixed point theorem infinite delay second-order integrodifferential equation impulsive measures of noncompactness mild solution resolvent operator |
| url | http://ejde.math.txstate.edu/Volumes/2025/54/abstr.html |
| work_keys_str_mv | AT abdelhamidbensalem optimalcontrolandapproximatecontrollabilityforsecondorderintegrodifferentialequationswithstatedependentdelayandnoninstantaneousimpulses AT abdelkrimsalim optimalcontrolandapproximatecontrollabilityforsecondorderintegrodifferentialequationswithstatedependentdelayandnoninstantaneousimpulses AT mouffakbenchohra optimalcontrolandapproximatecontrollabilityforsecondorderintegrodifferentialequationswithstatedependentdelayandnoninstantaneousimpulses AT gastonmnguerekata optimalcontrolandapproximatecontrollabilityforsecondorderintegrodifferentialequationswithstatedependentdelayandnoninstantaneousimpulses |