| ŠEPITKA, Peter and Roman ŠIMON HILSCHER. Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems. Journal of Differential Equations. San Diego: ACADEMIC PRESS INC ELSEVIER SCIENCE, 2019, vol. 266, No 11, p. 7481-7524. ISSN 0022-0396. Available from: https://dx.doi.org/10.1016/j.jde.2018.12.007. |
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@article{1475127,
author = {Šepitka, Peter and Šimon Hilscher, Roman},
article_location = {San Diego},
article_number = {11},
doi = {http://dx.doi.org/10.1016/j.jde.2018.12.007},
keywords = {Linear Hamiltonian system; Proper focal point; Principal solution; Antiprincipal solution; Controllability},
language = {eng},
issn = {0022-0396},
journal = {Journal of Differential Equations},
title = {Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems},
url = {https://www.sciencedirect.com/science/article/pii/S0022039618306958},
volume = {266},
year = {2019}
}
TY - JOUR
ID - 1475127
AU - Šepitka, Peter - Šimon Hilscher, Roman
PY - 2019
TI - Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems
JF - Journal of Differential Equations
VL - 266
IS - 11
SP - 7481-7524
EP - 7481-7524
PB - ACADEMIC PRESS INC ELSEVIER SCIENCE
SN - 00220396
KW - Linear Hamiltonian system
KW - Proper focal point
KW - Principal solution
KW - Antiprincipal solution
KW - Controllability
UR - https://www.sciencedirect.com/science/article/pii/S0022039618306958
L2 - https://www.sciencedirect.com/science/article/pii/S0022039618306958
N2 - In this paper we develop new fundamental results in the Sturmian theory for nonoscillatory linear Hamiltonian systems on an unbounded interval. We introduce a new concept of a multiplicity of a focal point at infinity for conjoined bases and, based on this notion, we prove singular Sturmian separation theorems on an unbounded interval. The main results are formulated in terms of the (minimal) principal solutions at both endpoints of the considered interval, and include exact formulas as well as optimal estimates for the numbers of proper focal points of one or two conjoined bases. As a natural tool we use the comparative index, which was recently implemented into the theory of linear Hamiltonian systems by the authors and independently by J. Elyseeva. Throughout the paper we do not assume any controllability condition on the system. Our results turn out to be new even in the completely controllable case.
ER -
ŠEPITKA, Peter and Roman ŠIMON HILSCHER. Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems. \textit{Journal of Differential Equations}. San Diego: ACADEMIC PRESS INC ELSEVIER SCIENCE, 2019, vol.~266, No~11, p.~7481-7524. ISSN~0022-0396. Available from: https://dx.doi.org/10.1016/j.jde.2018.12.007.
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