Weak disconjugacy, weak controllability, and genera of conjoined bases for linear Hamiltonian systems

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F22%3A00129036" target="_blank" >RIV/00216224:14310/22:00129036 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1007/s10231-022-01194-x" target="_blank" >https://link.springer.com/article/10.1007/s10231-022-01194-x</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10231-022-01194-x" target="_blank" >10.1007/s10231-022-01194-x</a>

Result language

angličtina

Original language name

Weak disconjugacy, weak controllability, and genera of conjoined bases for linear Hamiltonian systems

Original language description

In this paper, we discuss mutual interrelations between the notions of weak disconjugacy and weak controllability for linear Hamiltonian differential systems. These notions have been used in connection with the study of exponential dichotomy, nonoscillation, and dissipative control processes for these systems [e.g. (Johnson et al., in: Nonautonomous linear Hamiltonian systems: oscillation, spectral theory and control developments in mathematics, Springer, Cham, 2016)]. As our main results, we derive characterizations of the weak controllability and weak disconjugacy in terms of properties of certain subspaces arising in the recently introduced theory of genera of conjoined bases for linear Hamiltonian systems (Sepitka in J Dyn Differ Equ 32(3):1139-1155, 2020). We also present new results regarding the zero value of the maximal order of abnormality of the system in terms of a weak controllability condition, or in terms of a weak disconjugacy condition when the system is nonoscillatory and satisfies the Legendre condition. In our accompanying comments, we highlight the connections of the theory of genera of conjoined bases with the existence of principal solutions at infinity, which arise in the study of weakly disconjugate linear Hamiltonian systems. The results in this paper may be regarded as a completion and clarification of the previous considerations in the literature about the weak disconjugacy and weak controllability conditions for linear Hamiltonian systems [e.g. (Fabbri et al. in: J Math Anal Appl 380(2):853-864, 2011), (Johnson et al., in Nonautonomous linear Hamiltonian systems: oscillation, spectral theory and control developments in mathematics, Springer, Cham, 2016)].

Czech name

—

Czech description

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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/GA19-01246S" target="_blank" >GA19-01246S: New oscillation theory for linear Hamiltonian and symplectic systems</a><br>

Continuities

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

Publication year

2022

Confidentiality

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

Name of the periodical

Annali di Matematica Pura ed Applicata

ISSN

0373-3114

e-ISSN

1618-1891

Volume of the periodical

201

Issue of the periodical within the volume

5

Country of publishing house

DE - GERMANY

Number of pages

16

Pages from-to

2121-2136

UT code for WoS article

000751728400001

EID of the result in the Scopus database

2-s2.0-85124327775