Aronszajn-Hukuara type theorem for semilinear differential inclusions with nonlocal conditions
In this note we investigate the topological structure of the mild solution set of nonlocal Cauchy problems governed by semilinear differential inclusions in separable Banach spaces. We show that the mild solution set is a compact absolute retract (and then a continuum and $R_\delta$-set). As a parti...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2015-07-01
|
| 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=3781 |
| _version_ | 1797830632543354880 |
|---|---|
| author | Tiziana Cardinali Paola Rubbioni |
| author_facet | Tiziana Cardinali Paola Rubbioni |
| author_sort | Tiziana Cardinali |
| collection | DOAJ |
| description | In this note we investigate the topological structure of the mild solution set of nonlocal Cauchy problems governed by semilinear differential inclusions in separable Banach spaces. We show that the mild solution set is a compact absolute retract (and then a continuum and $R_\delta$-set). As a particular case, the topological structure of the periodic mild solution set is deduced. An illustrating example is supplied. |
| first_indexed | 2024-04-09T13:39:11Z |
| format | Article |
| id | doaj.art-2c301782bb00481c9fda0edff98eff30 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:39:11Z |
| publishDate | 2015-07-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-2c301782bb00481c9fda0edff98eff302023-05-09T07:53:04ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752015-07-0120154511210.14232/ejqtde.2015.1.453781Aronszajn-Hukuara type theorem for semilinear differential inclusions with nonlocal conditionsTiziana Cardinali0Paola Rubbioni1Department of Mathematics and Informatics, University of Perugia, ItalyDepartment of Mathematics and Informatics, University of Perugia, Perugia, ItalyIn this note we investigate the topological structure of the mild solution set of nonlocal Cauchy problems governed by semilinear differential inclusions in separable Banach spaces. We show that the mild solution set is a compact absolute retract (and then a continuum and $R_\delta$-set). As a particular case, the topological structure of the periodic mild solution set is deduced. An illustrating example is supplied.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3781nonlocal conditions; semilinear differential inclusions; mild solutions; periodic solutions; absolute retract |
| spellingShingle | Tiziana Cardinali Paola Rubbioni Aronszajn-Hukuara type theorem for semilinear differential inclusions with nonlocal conditions Electronic Journal of Qualitative Theory of Differential Equations nonlocal conditions; semilinear differential inclusions; mild solutions; periodic solutions; absolute retract |
| title | Aronszajn-Hukuara type theorem for semilinear differential inclusions with nonlocal conditions |
| title_full | Aronszajn-Hukuara type theorem for semilinear differential inclusions with nonlocal conditions |
| title_fullStr | Aronszajn-Hukuara type theorem for semilinear differential inclusions with nonlocal conditions |
| title_full_unstemmed | Aronszajn-Hukuara type theorem for semilinear differential inclusions with nonlocal conditions |
| title_short | Aronszajn-Hukuara type theorem for semilinear differential inclusions with nonlocal conditions |
| title_sort | aronszajn hukuara type theorem for semilinear differential inclusions with nonlocal conditions |
| topic | nonlocal conditions; semilinear differential inclusions; mild solutions; periodic solutions; absolute retract |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3781 |
| work_keys_str_mv | AT tizianacardinali aronszajnhukuaratypetheoremforsemilineardifferentialinclusionswithnonlocalconditions AT paolarubbioni aronszajnhukuaratypetheoremforsemilineardifferentialinclusionswithnonlocalconditions |