Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F19%3A00107205" target="_blank" >RIV/00216224:14310/19:00107205 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0022039618306958" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022039618306958</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2018.12.007" target="_blank" >10.1016/j.jde.2018.12.007</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems

Popis výsledku v původním jazyce

In this paper we develop new fundamental results in the Sturmian theory for nonoscillatory linear Hamiltonian systems on an unbounded interval. We introduce a new concept of a multiplicity of a focal point at infinity for conjoined bases and, based on this notion, we prove singular Sturmian separation theorems on an unbounded interval. The main results are formulated in terms of the (minimal) principal solutions at both endpoints of the considered interval, and include exact formulas as well as optimal estimates for the numbers of proper focal points of one or two conjoined bases. As a natural tool we use the comparative index, which was recently implemented into the theory of linear Hamiltonian systems by the authors and independently by J. Elyseeva. Throughout the paper we do not assume any controllability condition on the system. Our results turn out to be new even in the completely controllable case.

Název v anglickém jazyce

Singular Sturmian separation theorems on unbounded intervals for linear Hamiltonian systems

Popis výsledku anglicky

In this paper we develop new fundamental results in the Sturmian theory for nonoscillatory linear Hamiltonian systems on an unbounded interval. We introduce a new concept of a multiplicity of a focal point at infinity for conjoined bases and, based on this notion, we prove singular Sturmian separation theorems on an unbounded interval. The main results are formulated in terms of the (minimal) principal solutions at both endpoints of the considered interval, and include exact formulas as well as optimal estimates for the numbers of proper focal points of one or two conjoined bases. As a natural tool we use the comparative index, which was recently implemented into the theory of linear Hamiltonian systems by the authors and independently by J. Elyseeva. Throughout the paper we do not assume any controllability condition on the system. Our results turn out to be new even in the completely controllable case.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA16-00611S" target="_blank" >GA16-00611S: Hamiltonovské a symplektické systémy: oscilační a spektrální teorie</a><br>

Návaznosti

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

Rok uplatnění

2019

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

1090-2732

Svazek periodika

266

Číslo periodika v rámci svazku

11

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

44

Strana od-do

7481-7524

Kód UT WoS článku

000461048300020

EID výsledku v databázi Scopus

2-s2.0-85080043194