The Fucik spectrum of the discrete Dirichlet operator

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F18%3A43951130" target="_blank" >RIV/49777513:23520/18:43951130 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.laa.2018.04.017" target="_blank" >http://dx.doi.org/10.1016/j.laa.2018.04.017</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.laa.2018.04.017" target="_blank" >10.1016/j.laa.2018.04.017</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Fucik spectrum of the discrete Dirichlet operator

Popis výsledku v původním jazyce

In this paper, we deal with the discrete Dirichlet operator of the second order and we investigate its Fučík spectrum, which consists of a finite number of algebraic curves. For each non-trivial Fučík curve, we are able to detect a finite number of its points, which are given explicitely. We provide the exact implicit description of all non-trivial Fučík curves in terms of Chebyshev polynomials of the second kind. Moreover, for each non-trivial Fučík curve, we give several different implicit descriptions, which differ in the level of depth of used nested functions. Our approach is based on the Möbius transformation and on the appropriate continuous extension of solutions of the discrete problem. Let us note that all presented descriptions of Fučík curves have the form of necessary and sufficient conditions. Finally, our approach can be also directly used in the case of difference operators of the second order with other local boundary conditions.

Název v anglickém jazyce

The Fucik spectrum of the discrete Dirichlet operator

Popis výsledku anglicky

In this paper, we deal with the discrete Dirichlet operator of the second order and we investigate its Fučík spectrum, which consists of a finite number of algebraic curves. For each non-trivial Fučík curve, we are able to detect a finite number of its points, which are given explicitely. We provide the exact implicit description of all non-trivial Fučík curves in terms of Chebyshev polynomials of the second kind. Moreover, for each non-trivial Fučík curve, we give several different implicit descriptions, which differ in the level of depth of used nested functions. Our approach is based on the Möbius transformation and on the appropriate continuous extension of solutions of the discrete problem. Let us note that all presented descriptions of Fučík curves have the form of necessary and sufficient conditions. Finally, our approach can be also directly used in the case of difference operators of the second order with other local boundary conditions.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA13-00863S" target="_blank" >GA13-00863S: Semilineární a kvazilineární diferenciální rovnice: existence a násobnost řešení</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

LINEAR ALGEBRA AND ITS APPLICATIONS

ISSN

0024-3795

e-ISSN

—

Svazek periodika

553

Číslo periodika v rámci svazku

SEP 15 2018

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

46

Strana od-do

58-103

Kód UT WoS článku

000436050600004

EID výsledku v databázi Scopus

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