Global bifurcation diagrams of positive solutions for a class of 1D superlinear indefinite problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F22%3A43964021" target="_blank" >RIV/49777513:23520/22:43964021 - isvavai.cz</a>

Výsledek na webu

<a href="https://iopscience.iop.org/article/10.1088/1361-6544/ac4a88" target="_blank" >https://iopscience.iop.org/article/10.1088/1361-6544/ac4a88</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1361-6544/ac4a88" target="_blank" >10.1088/1361-6544/ac4a88</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Global bifurcation diagrams of positive solutions for a class of 1D superlinear indefinite problems

Popis výsledku v původním jazyce

This paper analyzes the structure of the set of positive solutions of a class of one-dimensional superlinear indefinite bvp’s. It is a paradigm of how mathematical analysis aids the numerical study of a problem,whereas simultaneously its numerical study confirms and illuminates the analysis. On the analytical side, we establish the fast decay of the positive solutions as λ ↓ −∞ in the region where a(x) &lt; 0 (see (1.1)), as well as the decay of the solutions of the parabolic counterpart of the model (see (1.2)) as λ ↓ −∞on any subinterval of [0, 1] where u0 = 0, provided u0 is a subsolution of (1.1). This result provides uswith a proof of a conjecture of [26] under an additional condition of a dynamical nature. On the numerical side, this paper ascertains the global structure of the set of positive solutions on some paradigmatic prototypes whose intricate behavior is far from predictable from existing analytical results.

Název v anglickém jazyce

Global bifurcation diagrams of positive solutions for a class of 1D superlinear indefinite problems

Popis výsledku anglicky

This paper analyzes the structure of the set of positive solutions of a class of one-dimensional superlinear indefinite bvp’s. It is a paradigm of how mathematical analysis aids the numerical study of a problem,whereas simultaneously its numerical study confirms and illuminates the analysis. On the analytical side, we establish the fast decay of the positive solutions as λ ↓ −∞ in the region where a(x) &lt; 0 (see (1.1)), as well as the decay of the solutions of the parabolic counterpart of the model (see (1.2)) as λ ↓ −∞on any subinterval of [0, 1] where u0 = 0, provided u0 is a subsolution of (1.1). This result provides uswith a proof of a conjecture of [26] under an additional condition of a dynamical nature. On the numerical side, this paper ascertains the global structure of the set of positive solutions on some paradigmatic prototypes whose intricate behavior is far from predictable from existing analytical results.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

NONLINEARITY

ISSN

0951-7715

e-ISSN

—

Svazek periodika

35

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

36

Strana od-do

1213-1248

Kód UT WoS článku

000749512400001

EID výsledku v databázi Scopus

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