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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

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

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

  • 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