Principal solutions at infinity for time scale symplectic systems without controllability condition
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F16%3A00088010" target="_blank" >RIV/00216224:14310/16:00088010 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2016.06.057" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2016.06.057</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2016.06.057" target="_blank" >10.1016/j.jmaa.2016.06.057</a>
Alternative languages
Result language
angličtina
Original language name
Principal solutions at infinity for time scale symplectic systems without controllability condition
Original language description
In this paper we introduce a new concept of a principal solution at infinity for nonoscillatory symplectic dynamic systems on time scales. The main ingredient is that we avoid the controllability (or normality) condition, which is traditionally assumed in this theory in the current literature. We show that the principal solutions at infinity can be classified according to the eventual rank of their first component and that the principal solutions exist for all values of the rank between explicitly given minimal and maximal values. The minimal value of the rank is connected with the eventual order of abnormality of the system and it gives rise to the so-called minimal principal solution at infinity. We show that the uniqueness property of the principal solutions at infinity is satisfied only by the minimal principal solution.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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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
2016
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 Mathematical Analysis and Applications
ISSN
0022-247X
e-ISSN
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Volume of the periodical
444
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
29
Pages from-to
852-880
UT code for WoS article
000381956400003
EID of the result in the Scopus database
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