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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

  • 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/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

  • 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