Eigenvalue theory for time scale symplectic systems depending nonlinearly on spectral parameter

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F12%3A00057514" target="_blank" >RIV/00216224:14310/12:00057514 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.amc.2012.08.026" target="_blank" >http://dx.doi.org/10.1016/j.amc.2012.08.026</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.amc.2012.08.026" target="_blank" >10.1016/j.amc.2012.08.026</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Eigenvalue theory for time scale symplectic systems depending nonlinearly on spectral parameter

Popis výsledku v původním jazyce

In this paper we develop the eigenvalue theory for general time scale symplectic systems, in which the dependence on the spectral parameter lambda is allowed to be nonlinear. At the same time we do not impose any controllability or strict normality assumptions. We prove the oscillation theorems for eigenvalue problems with Dirichlet, separated, and jointly varying endpoints, including the periodic boundary conditions. We also allow the boundary conditions depending on the spectral parameter. Our new theory generalizes and unifies recently published results on continuous-time linear Hamiltonian systems and discrete symplectic systems with nonlinear dependence on lambda and on time scale symplectic systems with linear dependence on lambda. The results ofthis paper are also new in the special case of linear Hamiltonian systems with variable endpoints, as well as for Sturm-Liouville dynamic equations.

Název v anglickém jazyce

Eigenvalue theory for time scale symplectic systems depending nonlinearly on spectral parameter

Popis výsledku anglicky

In this paper we develop the eigenvalue theory for general time scale symplectic systems, in which the dependence on the spectral parameter lambda is allowed to be nonlinear. At the same time we do not impose any controllability or strict normality assumptions. We prove the oscillation theorems for eigenvalue problems with Dirichlet, separated, and jointly varying endpoints, including the periodic boundary conditions. We also allow the boundary conditions depending on the spectral parameter. Our new theory generalizes and unifies recently published results on continuous-time linear Hamiltonian systems and discrete symplectic systems with nonlinear dependence on lambda and on time scale symplectic systems with linear dependence on lambda. The results ofthis paper are also new in the special case of linear Hamiltonian systems with variable endpoints, as well as for Sturm-Liouville dynamic equations.

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

<a href="/cs/project/GAP201%2F10%2F1032" target="_blank" >GAP201/10/1032: Diferenční rovnice a dynamické rovnice na ,,time scales'' III</a><br>

Návaznosti

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

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Applied Mathematics and Computation

ISSN

0096-3003

e-ISSN

—

Svazek periodika

219

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

2839-2860

Kód UT WoS článku

000310649900003

EID výsledku v databázi Scopus

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