Localization of Fučík curves for the second order discrete Dirichlet operator

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F21%3A43962114" target="_blank" >RIV/49777513:23520/21:43962114 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/abs/pii/S0007449721000701" target="_blank" >https://www.sciencedirect.com/science/article/abs/pii/S0007449721000701</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.bulsci.2021.103014" target="_blank" >10.1016/j.bulsci.2021.103014</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Localization of Fučík curves for the second order discrete Dirichlet operator

Popis výsledku v původním jazyce

In this paper, we deal with the second order difference equation with asymmetric nonlinearities on the integer lattice and we investigate the distribution of zeros for continuous extensions of positive semi-waves. The distance between two consecutive zeros of two different positive semi-waves depends not only on the parameters of the problem but also on the position of one of these zeros with respect to the integer lattice. We provide an explicit formula for this distance, which allows us to obtain a new simple implicit description of all non-trivial Fučík curves for the discrete Dirichlet operator. Moreover, for fixed parameters of the problem, we show that this distance is bounded and attains its global extrema that are explicitly described in terms of Chebyshev polynomials of the second kind. Finally, for each non-trivial Fučík curve, we provide suitable bounds by two curves with a simple description similar to the description of the first non-trivial Fučík curve.

Název v anglickém jazyce

Localization of Fučík curves for the second order discrete Dirichlet operator

Popis výsledku anglicky

In this paper, we deal with the second order difference equation with asymmetric nonlinearities on the integer lattice and we investigate the distribution of zeros for continuous extensions of positive semi-waves. The distance between two consecutive zeros of two different positive semi-waves depends not only on the parameters of the problem but also on the position of one of these zeros with respect to the integer lattice. We provide an explicit formula for this distance, which allows us to obtain a new simple implicit description of all non-trivial Fučík curves for the discrete Dirichlet operator. Moreover, for fixed parameters of the problem, we show that this distance is bounded and attains its global extrema that are explicitly described in terms of Chebyshev polynomials of the second kind. Finally, for each non-trivial Fučík curve, we provide suitable bounds by two curves with a simple description similar to the description of the first non-trivial Fučík curve.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-03253S" target="_blank" >GA18-03253S: Diferenciální rovnice se speciálními typy nelinearit</a><br>

Návaznosti

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

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

BULLETIN DES SCIENCES MATHEMATIQUES

ISSN

0007-4497

e-ISSN

—

Svazek periodika

171

Číslo periodika v rámci svazku

October 2021

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

51

Strana od-do

—

Kód UT WoS článku

000686234600001

EID výsledku v databázi Scopus

2-s2.0-85108295546