| DŘÍMALOVÁ, Iva a Roman ŠIMON HILSCHER. Antiprincipal solutions at infinity for symplectic systems on time scales. Electronic Journal of Qualitative Theory of Differential Equations. Szeged: University of Szeged, 2020, Neuveden, č. 44, s. 1-32. ISSN 1417-3875. Dostupné z: https://dx.doi.org/10.14232/ejqtde.2020.1.44. |
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@article{1668621,
author = {Dřímalová, Iva and Šimon Hilscher, Roman},
article_location = {Szeged},
article_number = {44},
doi = {http://dx.doi.org/10.14232/ejqtde.2020.1.44},
keywords = {Symplectic system on time scale; Antiprincipal solution at infinity; Principal solution at infinity; Nonoscillation; Linear Hamiltonian system; Normality},
language = {eng},
issn = {1417-3875},
journal = {Electronic Journal of Qualitative Theory of Differential Equations},
title = {Antiprincipal solutions at infinity for symplectic systems on time scales},
url = {http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8447},
volume = {Neuveden},
year = {2020}
}
TY - JOUR
ID - 1668621
AU - Dřímalová, Iva - Šimon Hilscher, Roman
PY - 2020
TI - Antiprincipal solutions at infinity for symplectic systems on time scales
JF - Electronic Journal of Qualitative Theory of Differential Equations
VL - Neuveden
IS - 44
SP - 1-32
EP - 1-32
PB - University of Szeged
SN - 14173875
KW - Symplectic system on time scale
KW - Antiprincipal solution at infinity
KW - Principal solution at infinity
KW - Nonoscillation
KW - Linear Hamiltonian system
KW - Normality
UR - http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8447
L2 - http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8447
N2 - 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 Sepitka (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.
ER -
DŘÍMALOVÁ, Iva a Roman ŠIMON HILSCHER. Antiprincipal solutions at infinity for symplectic systems on time scales. \textit{Electronic Journal of Qualitative Theory of Differential Equations}. Szeged: University of Szeged, 2020, Neuveden, č.~44, s.~1-32. ISSN~1417-3875. Dostupné z: https://dx.doi.org/10.14232/ejqtde.2020.1.44.
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