Antiprincipal solutions at infinity for symplectic systems on
time scales

J 2020

Antiprincipal solutions at infinity for symplectic systems on time scales

DŘÍMALOVÁ, Iva a Roman ŠIMON HILSCHER

Základní údaje

Originální název

Antiprincipal solutions at infinity for symplectic systems on time scales

Autoři

DŘÍMALOVÁ, Iva a Roman ŠIMON HILSCHER

Vydání

Electronic Journal of Qualitative Theory of Differential Equations, Szeged, University of Szeged, 2020, 1417-3875

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Maďarsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

Full text

Impakt faktor

Impact factor: 1.874

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/20:00114213

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Symplectic system on time scale; Antiprincipal solution at infinity; Principal solution at infinity; Nonoscillation; Linear Hamiltonian system; Normality

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 24. 11. 2020 10:06, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Návaznosti

GA19-01246S, projekt VaV

Název: Nová oscilační teorie pro lineární hamiltonovské a symplektické systémy

Investor: Grantová agentura ČR, Nová oscilační teorie pro lineární hamiltonovské a symplektické systémy

Citovat

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://doi.org/10.14232/ejqtde.2020.1.44.

@article{1668621,
   author = {Dřímalová, Iva and Šimon Hilscher, Roman},
   article_location = {Szeged},
   article_number = {44},
   doi = {https://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://doi.org/10.14232/ejqtde.2020.1.44.

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