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@article{2314737,
author = {Dřímalová, Iva},
article_number = {3},
doi = {http://dx.doi.org/10.7153/dea-2023-15-11},
keywords = {Symplectic system on time scale; genus of conjoined bases; antiprincipal solution at infinity; principal solution at infinity; nonoscillation; Riccati matrix dynamic equation; Moore–Penrose pseudoinverse},
language = {eng},
issn = {1847-120X},
journal = {Differential Equations & Applications},
title = {Extremal solutions at infinity for symplectic systems on time scales II - Existence theory and limit properties},
url = {http://dx.doi.org/10.7153/dea-2023-15-11},
volume = {15},
year = {2023}
}
TY - JOUR
ID - 2314737
AU - Dřímalová, Iva
PY - 2023
TI - Extremal solutions at infinity for symplectic systems on time scales II - Existence theory and limit properties
JF - Differential Equations & Applications
VL - 15
IS - 3
SP - 179-213
EP - 179-213
PB - Element
SN - 1847120X
KW - Symplectic system on time scale
KW - genus of conjoined bases
KW - antiprincipal solution at infinity
KW - principal solution at infinity
KW - nonoscillation
KW - Riccati matrix dynamic equation
KW - Moore–Penrose pseudoinverse
UR - http://dx.doi.org/10.7153/dea-2023-15-11
N2 - In this paper we continue with our investigation of principal and antiprincipal solutions at infinity solutions of a dynamic symplectic system. The paper is a continuation of part I appeared in Differential Equations and Applications in 2022, where we have presenteded a theory of genera of conjoined bases for symplectic dynamic systems on time scales and its connections with principal solutions at infinity and antiprincipal solutions at infinity for these systems together with some basic properties of this new concept on time scales. Here we provide a characterization of all principal solutions of dynamic symplectic system at infinity in the given genus in terms of the initial conditions and a fixed principal solution at infinity from this genus. Further, we provide a characterization of all antiprincipal solutions of dynamic symplectic system at infinity in the given genus in terms of the initial conditions and a fixed principal solution at infinity from this genus. We also establish mutual limit properties of principal and antiprincipal solutions at infinity.
ER -
DŘÍMALOVÁ, Iva. Extremal solutions at infinity for symplectic systems on time scales II - Existence theory and limit properties. \textit{Differential Equations \&{} Applications}. Element, 2023, roč.~15, č.~3, s.~179-213. ISSN~1847-120X. Dostupné z: https://dx.doi.org/10.7153/dea-2023-15-11.
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