Principal and antiprincipal solutions at infinity of linear Hamiltonian systems

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Principal and antiprincipal solutions at infinity of linear Hamiltonian systems

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Principal and antiprincipal solutions at infinity of linear Hamiltonian systems

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GAP201%2F10%2F1032" target="_blank" >GAP201/10/1032: Diferenční rovnice a dynamické rovnice na ,,time scales'' III</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

—

Svazek periodika

259

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

32

Strana od-do

4651-4682

Kód UT WoS článku

000359507800007

EID výsledku v databázi Scopus

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