Singular Sturmian separation theorems for nonoscillatory symplectic difference systems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F18%3A00101296" target="_blank" >RIV/00216224:14310/18:00101296 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1080/10236198.2018.1544247" target="_blank" >http://dx.doi.org/10.1080/10236198.2018.1544247</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1080/10236198.2018.1544247" target="_blank" >10.1080/10236198.2018.1544247</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Singular Sturmian separation theorems for nonoscillatory symplectic difference systems

Popis výsledku v původním jazyce

In this paper we derive new singular Sturmian separation theorems for nonoscillatory symplectic difference systems on unbounded intervals. The novelty of the presented theory resides in two aspects. We introduce the multiplicity of a focal point at infinity for conjoined bases, which we incorporate into our new singular Sturmian separation theorems. At the same time we do not impose any controllability assumption on the symplectic system. The presented results naturally extend and complete the known Sturmian separation theorems on bounded intervals by J. Elyseeva (2009), as well as the singular Sturmian separation theorems for eventually controllable symplectic systems on unbounded intervals by O. Dosly and J. Elyseeva (2014). Our approach is based on developing the theory of comparative index on unbounded intervals and on the recent theory of recessive and dominant solutions at infinity for possibly uncontrollable symplectic systems by the authors (2015 and 2017). Some of our results, including the notion of the multiplicity of a focal point at infinity, are new even for an eventually controllable symplectic difference system.

Název v anglickém jazyce

Singular Sturmian separation theorems for nonoscillatory symplectic difference systems

Popis výsledku anglicky

In this paper we derive new singular Sturmian separation theorems for nonoscillatory symplectic difference systems on unbounded intervals. The novelty of the presented theory resides in two aspects. We introduce the multiplicity of a focal point at infinity for conjoined bases, which we incorporate into our new singular Sturmian separation theorems. At the same time we do not impose any controllability assumption on the symplectic system. The presented results naturally extend and complete the known Sturmian separation theorems on bounded intervals by J. Elyseeva (2009), as well as the singular Sturmian separation theorems for eventually controllable symplectic systems on unbounded intervals by O. Dosly and J. Elyseeva (2014). Our approach is based on developing the theory of comparative index on unbounded intervals and on the recent theory of recessive and dominant solutions at infinity for possibly uncontrollable symplectic systems by the authors (2015 and 2017). Some of our results, including the notion of the multiplicity of a focal point at infinity, are new even for an eventually controllable symplectic difference system.

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

2018

Kód důvěrnosti údajů

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

Název periodika

Journal of Difference Equations and Applications

ISSN

1023-6198

e-ISSN

1563-5120

Svazek periodika

24

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

41

Strana od-do

1894-1934

Kód UT WoS článku

000455587900004

EID výsledku v databázi Scopus

2-s2.0-85057566926