On nonlocal problems for semilinear second order differential inclusions without compactness
Existence of mild solutions for a nonlocal abstract problem driven by a semilinear second order differential inclusion is studied in Banach spaces in the lack of compactness both on the fundamental system generated by the linear part and on the nonlinear multivalued term. The method used for proving...
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| Format: | Article |
| Language: | English |
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University of Szeged
2021-09-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9261 |
| _version_ | 1797830463314722816 |
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| author | Tiziana Cardinali Giulia Duricchi |
| author_facet | Tiziana Cardinali Giulia Duricchi |
| author_sort | Tiziana Cardinali |
| collection | DOAJ |
| description | Existence of mild solutions for a nonlocal abstract problem driven by a semilinear second order differential inclusion is studied in Banach spaces in the lack of compactness both on the fundamental system generated by the linear part and on the nonlinear multivalued term. The method used for proving our existence theorems is based on the combination of a fixed point theorem and a selection theorem developed by ourselves with an approach that uses De Blasi measure of noncompactness and the weak topology. As application of our existence result we present the study of the controllability of a problem guided by a wave equation. |
| first_indexed | 2024-04-09T13:36:28Z |
| format | Article |
| id | doaj.art-bf3458e953d6429eaae7a468f41873fc |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:36:28Z |
| publishDate | 2021-09-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-bf3458e953d6429eaae7a468f41873fc2023-05-09T07:53:11ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752021-09-0120216613210.14232/ejqtde.2021.1.669261On nonlocal problems for semilinear second order differential inclusions without compactnessTiziana Cardinali0Giulia Duricchi1Dept. of Mathematics and Computer Sciences, University of Perugia, 1, via Vanvitelli, 06123 Perugia, ItalyDept. of Mathematics and Computer Sciences, University of Perugia, 1, via Vanvitelli, 06123 Perugia, ItalyExistence of mild solutions for a nonlocal abstract problem driven by a semilinear second order differential inclusion is studied in Banach spaces in the lack of compactness both on the fundamental system generated by the linear part and on the nonlinear multivalued term. The method used for proving our existence theorems is based on the combination of a fixed point theorem and a selection theorem developed by ourselves with an approach that uses De Blasi measure of noncompactness and the weak topology. As application of our existence result we present the study of the controllability of a problem guided by a wave equation.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9261nonlocal abstract problemsemilinear second order differential inclusionfundamental systemde blasi measure of noncompactnesscontrollability problemwave equation |
| spellingShingle | Tiziana Cardinali Giulia Duricchi On nonlocal problems for semilinear second order differential inclusions without compactness Electronic Journal of Qualitative Theory of Differential Equations nonlocal abstract problem semilinear second order differential inclusion fundamental system de blasi measure of noncompactness controllability problem wave equation |
| title | On nonlocal problems for semilinear second order differential inclusions without compactness |
| title_full | On nonlocal problems for semilinear second order differential inclusions without compactness |
| title_fullStr | On nonlocal problems for semilinear second order differential inclusions without compactness |
| title_full_unstemmed | On nonlocal problems for semilinear second order differential inclusions without compactness |
| title_short | On nonlocal problems for semilinear second order differential inclusions without compactness |
| title_sort | on nonlocal problems for semilinear second order differential inclusions without compactness |
| topic | nonlocal abstract problem semilinear second order differential inclusion fundamental system de blasi measure of noncompactness controllability problem wave equation |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9261 |
| work_keys_str_mv | AT tizianacardinali onnonlocalproblemsforsemilinearsecondorderdifferentialinclusionswithoutcompactness AT giuliaduricchi onnonlocalproblemsforsemilinearsecondorderdifferentialinclusionswithoutcompactness |