Antiprincipal solutions at infinity for symplectic systems on time scales
In this paper we introduce a new concept of antiprincipal solutions at infinity for symplectic systems on time scales. This concept complements the earlier notion of principal solutions at infinity for these systems by the second author and Šepitka (2016). We derive main properties of antiprincipa...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2020-06-01
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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=8447 |
| _version_ | 1797830531482648576 |
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| author | Iva Drimalova Roman Simon Hilscher |
| author_facet | Iva Drimalova Roman Simon Hilscher |
| author_sort | Iva Drimalova |
| collection | DOAJ |
| description | In this paper we introduce a new concept of antiprincipal solutions at infinity for symplectic systems on time scales. This concept complements the earlier notion of principal solutions at infinity for these systems by the second author and Šepitka (2016). We derive main properties of antiprincipal solutions at infinity, including their existence for all ranks in a given range and a~construction from a certain minimal antiprincipal solution at infinity. We apply our new theory of antiprincipal solutions at infinity in the study of principal solutions, and in particular in the Reid construction of the minimal principal solution at infinity. In this work we do not assume any normality condition on the system, and we unify and extend to arbitrary time scales the theory of antiprincipal solutions at infinity of linear Hamiltonian differential systems and the theory of dominant solutions at infinity of symplectic difference systems. |
| first_indexed | 2024-04-09T13:37:37Z |
| format | Article |
| id | doaj.art-b2bfa03ed358456aaeed1cbcce934bc4 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:37Z |
| publishDate | 2020-06-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-b2bfa03ed358456aaeed1cbcce934bc42023-05-09T07:53:10ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752020-06-0120204413210.14232/ejqtde.2020.1.448447Antiprincipal solutions at infinity for symplectic systems on time scalesIva Drimalova0Roman Simon Hilscher1Department of Mathematics and Statistics, Masaryk University, Brno, Czech RepublicMasaryk University, Brno, Czech RepublicIn this paper we introduce a new concept of antiprincipal solutions at infinity for symplectic systems on time scales. This concept complements the earlier notion of principal solutions at infinity for these systems by the second author and Šepitka (2016). We derive main properties of antiprincipal solutions at infinity, including their existence for all ranks in a given range and a~construction from a certain minimal antiprincipal solution at infinity. We apply our new theory of antiprincipal solutions at infinity in the study of principal solutions, and in particular in the Reid construction of the minimal principal solution at infinity. In this work we do not assume any normality condition on the system, and we unify and extend to arbitrary time scales the theory of antiprincipal solutions at infinity of linear Hamiltonian differential systems and the theory of dominant solutions at infinity of symplectic difference systems.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8447symplectic system on time scaleantiprincipal solution at infinityprincipal solution at infinitynonoscillationlinear hamiltonian systemnormality |
| spellingShingle | Iva Drimalova Roman Simon Hilscher Antiprincipal solutions at infinity for symplectic systems on time scales Electronic Journal of Qualitative Theory of Differential Equations symplectic system on time scale antiprincipal solution at infinity principal solution at infinity nonoscillation linear hamiltonian system normality |
| title | Antiprincipal solutions at infinity for symplectic systems on time scales |
| title_full | Antiprincipal solutions at infinity for symplectic systems on time scales |
| title_fullStr | Antiprincipal solutions at infinity for symplectic systems on time scales |
| title_full_unstemmed | Antiprincipal solutions at infinity for symplectic systems on time scales |
| title_short | Antiprincipal solutions at infinity for symplectic systems on time scales |
| title_sort | antiprincipal solutions at infinity for symplectic systems on time scales |
| topic | symplectic system on time scale antiprincipal solution at infinity principal solution at infinity nonoscillation linear hamiltonian system normality |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8447 |
| work_keys_str_mv | AT ivadrimalova antiprincipalsolutionsatinfinityforsymplecticsystemsontimescales AT romansimonhilscher antiprincipalsolutionsatinfinityforsymplecticsystemsontimescales |