Focal points and principal solutions of linear Hamiltonian systems revisited

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F18%3A00100766" target="_blank" >RIV/00216224:14310/18:00100766 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1016/j.jde.2018.01.016" target="_blank" >http://dx.doi.org/10.1016/j.jde.2018.01.016</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2018.01.016" target="_blank" >10.1016/j.jde.2018.01.016</a>

Result language

angličtina

Original language name

Focal points and principal solutions of linear Hamiltonian systems revisited

Original language description

In this paper we present a novel view on the principal (and antiprincipal) solutions of linear Hamiltonian systems, as well as on the focal points of their conjoined bases. We present a new and unified theory of principal (and antiprincipal) solutions at a finite point and at infinity, and apply it to obtain new representation of the multiplicities of right and left proper focal points of conjoined bases. We show that these multiplicities can be characterized by the abnormality of the system in a neighborhood of the given point and by the rank of the associated T-matrix from the theory of principal (and antiprincipal) solutions. We also derive some additional important results concerning the representation of T-matrices and associated normalized conjoined bases. The results in this paper are new even for completely controllable linear Hamiltonian systems. We also discuss other potential applications of our main results, in particular in the singular Sturmian theory.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GA16-00611S" target="_blank" >GA16-00611S: Hamiltonian and symplectic systems: oscillation and spectral theory</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2018

Confidentiality

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

Name of the periodical

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

—

Volume of the periodical

264

Issue of the periodical within the volume

9

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

36

Pages from-to

5541-5576

UT code for WoS article

000426147300002

EID of the result in the Scopus database

2-s2.0-85040322598