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
—