Principal solutions at infinity of given ranks for nonoscillatory linear Hamiltonian systems

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Principal solutions at infinity of given ranks for nonoscillatory linear Hamiltonian systems

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Principal solutions at infinity of given ranks for nonoscillatory linear Hamiltonian systems

Popis výsledku anglicky

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.

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 Dynamics and Differential Equations

ISSN

1040-7294

e-ISSN

—

Svazek periodika

27

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

39

Strana od-do

137-175

Kód UT WoS článku

000350823100006

EID výsledku v databázi Scopus

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