Recessive solutions for nonoscillatory discrete symplectic systems

Kód výsledku v IS VaVaI

RIV/00216224:14310/15:00080614 - isvavai.cz

Výsledek na webu

http://dx.doi.org/10.1016/j.laa.2014.11.029

DOI - Digital Object Identifier

10.1016/j.laa.2014.11.029

Jazyk výsledku

angličtina

Název v původním jazyce

Recessive solutions for nonoscillatory discrete symplectic systems

Popis výsledku v původním jazyce

In this paper we introduce a new concept of a recessive solution for discrete symplectic systems, which does not require any eventual controllability assumption. We prove that the existence of a recessive solution is equivalent with the nonoscillation ofthe system and that recessive solutions can have any rank between explicitly given lower and upper bounds. The smallest rank corresponds to the minimal recessive solution, which is unique up to a right nonsingular multiple, while the largest rank yieldsthe traditional maximal recessive solution. We also present a method for constructing some (but not all) recessive solutions having a block diagonal structure from systems in lower dimension. Our results are new even for special discrete symplectic systems, such as for even order Sturm--Liouville difference equations and linear Hamiltonian difference systems.

Název v anglickém jazyce

Recessive solutions for nonoscillatory discrete symplectic systems

Popis výsledku anglicky

In this paper we introduce a new concept of a recessive solution for discrete symplectic systems, which does not require any eventual controllability assumption. We prove that the existence of a recessive solution is equivalent with the nonoscillation ofthe system and that recessive solutions can have any rank between explicitly given lower and upper bounds. The smallest rank corresponds to the minimal recessive solution, which is unique up to a right nonsingular multiple, while the largest rank yieldsthe traditional maximal recessive solution. We also present a method for constructing some (but not all) recessive solutions having a block diagonal structure from systems in lower dimension. Our results are new even for special discrete symplectic systems, such as for even order Sturm--Liouville difference equations and linear Hamiltonian difference systems.

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

GAP201/10/1032: Diferenční rovnice a dynamické rovnice na ,,time scales'' III

Návaznosti

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

Linear Algebra and Its Applications

ISSN

0024-3795

e-ISSN

—

Svazek periodika

469

Číslo periodika v rámci svazku

March

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

33

Strana od-do

243-275

Kód UT WoS článku

000348883600012

EID výsledku v databázi Scopus

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