Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F19%3A00107205" target="_blank" >RIV/00216224:14310/19:00107205 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0022039618306958" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022039618306958</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2018.12.007" target="_blank" >10.1016/j.jde.2018.12.007</a>
Alternative languages
Result language
angličtina
Original language name
Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA16-00611S" target="_blank" >GA16-00611S: Hamiltonian and symplectic systems: oscillation and spectral theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Differential Equations
ISSN
0022-0396
e-ISSN
1090-2732
Volume of the periodical
266
Issue of the periodical within the volume
11
Country of publishing house
US - UNITED STATES
Number of pages
44
Pages from-to
7481-7524
UT code for WoS article
000461048300020
EID of the result in the Scopus database
2-s2.0-85080043194