Oscillation and spectral theory of Sturm-Liouville differential equations with nonlinear dependence in spectral parameter

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F13%3A00066009" target="_blank" >RIV/00216224:14310/13:00066009 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Oscillation and spectral theory of Sturm-Liouville differential equations with nonlinear dependence in spectral parameter

Popis výsledku v původním jazyce

In this paper, we consider the eigenvalue problem for the second order Sturm-Liouville differential equation and the Dirichlet boundary conditions. Our setting is more general than in the current literature in two respects: (i) the coefficients depend onthe spectral parameter lambda in general nonlinearly, and (ii) the potential is merely monotone in lambda and not necessarily strictly monotone in lambda, so that the usual strict normality assumption is now removed. This general setting leads to new definitions of an eigenvalue and an eigenfunction - called a finite eigenvalue and a finite eigenfunction. With these new concepts we show that the finite eigenvalues are isolated, bounded from below, and establish an oscillation theorem, i.e., a result counting the zeros of the finite eigenfunctions. The traditional theory in which the potential is linear and strictly monotone in lambda nicely follows from our results.

Název v anglickém jazyce

Oscillation and spectral theory of Sturm-Liouville differential equations with nonlinear dependence in spectral parameter

Popis výsledku anglicky

In this paper, we consider the eigenvalue problem for the second order Sturm-Liouville differential equation and the Dirichlet boundary conditions. Our setting is more general than in the current literature in two respects: (i) the coefficients depend onthe spectral parameter lambda in general nonlinearly, and (ii) the potential is merely monotone in lambda and not necessarily strictly monotone in lambda, so that the usual strict normality assumption is now removed. This general setting leads to new definitions of an eigenvalue and an eigenfunction - called a finite eigenvalue and a finite eigenfunction. With these new concepts we show that the finite eigenvalues are isolated, bounded from below, and establish an oscillation theorem, i.e., a result counting the zeros of the finite eigenfunctions. The traditional theory in which the potential is linear and strictly monotone in lambda nicely follows from our results.

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)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2013

Kód důvěrnosti údajů

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

Název periodika

Dynamic Systems and Applications

ISSN

1056-2176

e-ISSN

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Svazek periodika

22

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

10

Strana od-do

115-124

Kód UT WoS článku

000328805600008

EID výsledku v databázi Scopus

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