Extremal solutions at infinity for symplectic systems on time scales I – Genera of conjoined bases
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F22%3A00134003" target="_blank" >RIV/00216224:14310/22:00134003 - isvavai.cz</a>
Result on the web
<a href="http://dea.ele-math.com/14-07/Extremal-solutions-at-infinity-for-symplectic-systems-on-time-scales-I-Genera-of-conjoined-bases" target="_blank" >http://dea.ele-math.com/14-07/Extremal-solutions-at-infinity-for-symplectic-systems-on-time-scales-I-Genera-of-conjoined-bases</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.7153/dea-2022-14-07" target="_blank" >10.7153/dea-2022-14-07</a>
Alternative languages
Result language
angličtina
Original language name
Extremal solutions at infinity for symplectic systems on time scales I – Genera of conjoined bases
Original language description
In this paper we present a theory of genera of conjoined bases for symplectic dynamic systems on time scales and its connections with principal solutions at infinity and antiprincipal solutions at infinity for these systems. Among other properties we prove the existence of these extremal solutions in every genus. Our results generalize and complete the results by several authors on this subject, in particular by Došlý (2000), Šepitka and Šimon Hilscher (2016), and the author and Šimon Hilscher (2020). Some of our result are new even within the theory of genera of conjoined bases for linear Hamiltonian differential systems and symplectic difference systems, or they complete the arguments presented therein. Throughout the paper we do not assume any normality (controllability) condition on the system. This approach requires using the Moore–Penrose pseudoinverse matrices in the situations, where the inverse matrices occurred in the traditional literature. In this context we also prove a new explicit formula for the delta derivative of the Moore–Penrose pseudoinverse. This paper is a first part of the results connected with the theory of genera. The second part would naturally continue by providing a characterization of all principal solutions of (S) at infinity in the given genus in terms of the initial conditions and a fixed principal solution at infinity from this genus and focusing on limit properties of above mentioned special solutions and by establishing their limit comparison at infinity.
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
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Differential Equations & Applications
ISSN
1847-120X
e-ISSN
1848-9605
Volume of the periodical
14
Issue of the periodical within the volume
1
Country of publishing house
HR - CROATIA
Number of pages
38
Pages from-to
99-136
UT code for WoS article
000786361400001
EID of the result in the Scopus database
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