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Principal and antiprincipal solutions at infinity of 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%3A00080831" target="_blank" >RIV/00216224:14310/15:00080831 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.1016/j.jde.2015.06.027" target="_blank" >http://dx.doi.org/10.1016/j.jde.2015.06.027</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1016/j.jde.2015.06.027" target="_blank" >10.1016/j.jde.2015.06.027</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Principal and antiprincipal solutions at infinity of linear Hamiltonian systems

  • Original language description

    The concept of principal solutions at infinity for possibly abnormal linear Hamiltonian systems was recently introduced by the authors. In this paper we develop the theory of antiprincipal solutions at infinity and establish a limit characterization of the principal solutions. That is, we prove that the principal solutions are the smallest ones at infinity when they are compared with the antiprincipal solutions. This statement is a generalization of the classical result of W. T. Reid, P. Hartman, or W.A. Coppel for controllable linear Hamiltonian systems. We also derive a classification of antiprincipal solutions at infinity according to their rank and show that the antiprincipal solutions exist for any rank in the range between explicitly given minimal and maximal values. 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 Differential Equations

  • ISSN

    0022-0396

  • e-ISSN

  • Volume of the periodical

    259

  • Issue of the periodical within the volume

    9

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    32

  • Pages from-to

    4651-4682

  • UT code for WoS article

    000359507800007

  • EID of the result in the Scopus database