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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

  • Czech description

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/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