Principal solutions at infinity of given ranks for nonoscillatory 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%2F15%3A00080584" target="_blank" >RIV/00216224:14310/15:00080584 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10884-014-9389-7" target="_blank" >http://dx.doi.org/10.1007/s10884-014-9389-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10884-014-9389-7" target="_blank" >10.1007/s10884-014-9389-7</a>
Alternative languages
Result language
angličtina
Original language name
Principal solutions at infinity of given ranks for nonoscillatory linear Hamiltonian systems
Original language description
In this paper we study the existence and properties of the principal solutions at infinity of nonoscillatory linear Hamiltonian systems without any controllability assumption. As our main results we prove that the principal solutions can be classified according to the rank of their first component and that the principal solutions exist for any rank in the range between explicitly given minimal and maximal values. The minimal rank then corresponds to the minimal principal solution at infinity introducedby the authors in their previous paper, while the maximal rank corresponds to the principal solution at infinity developed by W.T.Reid, P.Hartman or W.A.Coppel. We also derive a classification of the principal solutions, which have eventually the same image. The proofs are based on a detailed analysis of conjoined bases with a given rank and their construction from the minimal conjoined bases. We illustrate our new theory by several examples.
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/GAP201%2F10%2F1032" target="_blank" >GAP201/10/1032: Difference equations and dynamic equations on time scales III</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach
Others
Publication year
2015
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 Dynamics and Differential Equations
ISSN
1040-7294
e-ISSN
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Volume of the periodical
27
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
39
Pages from-to
137-175
UT code for WoS article
000350823100006
EID of the result in the Scopus database
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