Singular Sturmian comparison theorems 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%2F20%3A00114052" target="_blank" >RIV/00216224:14310/20:00114052 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0022039620300802?dgcid=author" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022039620300802?dgcid=author</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2020.02.016" target="_blank" >10.1016/j.jde.2020.02.016</a>
Alternative languages
Result language
angličtina
Original language name
Singular Sturmian comparison theorems for linear Hamiltonian systems
Original language description
In this paper we prove singular comparison theorems on unbounded intervals for two nonoscillatory linear Hamiltonian systems satisfying the Sturmian majorant condition and the Legendre condition. At the same time we do not impose any controllability condition. The results are phrased in terms of the comparative index and the numbers of proper focal points of the (minimal) principal solutions of these systems at both endpoints of the considered interval. The main idea is based on an application of new transformation theorems for principal and antiprincipal solutions at infinity and on new limit properties of the comparative index involving these solutions. This work generalizes the recently obtained Sturmian separation theorems on unbounded intervals for one system by the authors (2019), as well as the Sturmian comparison theorems and transformation theorems on compact intervals by J. Elyseeva (2016 and 2018). We note that all the results are 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
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA19-01246S" target="_blank" >GA19-01246S: New oscillation theory for linear Hamiltonian and symplectic systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
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
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Volume of the periodical
269
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
36
Pages from-to
2920-2955
UT code for WoS article
000534488300007
EID of the result in the Scopus database
2-s2.0-85080043194