Existence and Multiplicity Results for Nonlocal Lane-Emden Systems
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00134083" target="_blank" >RIV/00216224:14310/23:00134083 - isvavai.cz</a>
Výsledek na webu
<a href="https://doi.org/10.1007/s40306-022-00485-y" target="_blank" >https://doi.org/10.1007/s40306-022-00485-y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s40306-022-00485-y" target="_blank" >10.1007/s40306-022-00485-y</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Existence and Multiplicity Results for Nonlocal Lane-Emden Systems
Popis výsledku v původním jazyce
In this work, we show the existence and multiplicity for the nonlocal Lane-Emden system of the form begin{array}{@{}rcl@{}} left{ begin{aligned} mathbb L u &= v^{p} + rho nu quad &&text{in } {varOmega}, mathbb L v &= u^{q} + sigma tau quad &&text{in } {varOmega}, u&=v = 0 quad &&text{on } partial {varOmega} text{ or in } {varOmega}^{c} text{ if applicable}, end{aligned} right. end{array} where {varOmega } subset mathbb {R}^{N} is a C2 bounded domain, mathbb L is a nonlocal operator, ν,τ are Radon measures on Ω, p,q are positive exponents, and ρ,σ > 0 are positive parameters. Based on a fine analysis of the interaction between the Green kernel associated with mathbb L, the source terms uq,vp and the measure data, we prove the existence of a positive minimal solution. Furthermore, by analyzing the geometry of Palais-Smale sequences in finite dimensional spaces given by the Galerkin type approximations and their appropriate uniform estimates, we establish the existence of a second positive solution, under a smallness condition on the positive parameters ρ,σ and superlinear growth conditions on source terms. The contribution of the paper lies on our unifying technique that is applicable to various types of local and nonlocal operators.
Název v anglickém jazyce
Existence and Multiplicity Results for Nonlocal Lane-Emden Systems
Popis výsledku anglicky
In this work, we show the existence and multiplicity for the nonlocal Lane-Emden system of the form begin{array}{@{}rcl@{}} left{ begin{aligned} mathbb L u &= v^{p} + rho nu quad &&text{in } {varOmega}, mathbb L v &= u^{q} + sigma tau quad &&text{in } {varOmega}, u&=v = 0 quad &&text{on } partial {varOmega} text{ or in } {varOmega}^{c} text{ if applicable}, end{aligned} right. end{array} where {varOmega } subset mathbb {R}^{N} is a C2 bounded domain, mathbb L is a nonlocal operator, ν,τ are Radon measures on Ω, p,q are positive exponents, and ρ,σ > 0 are positive parameters. Based on a fine analysis of the interaction between the Green kernel associated with mathbb L, the source terms uq,vp and the measure data, we prove the existence of a positive minimal solution. Furthermore, by analyzing the geometry of Palais-Smale sequences in finite dimensional spaces given by the Galerkin type approximations and their appropriate uniform estimates, we establish the existence of a second positive solution, under a smallness condition on the positive parameters ρ,σ and superlinear growth conditions on source terms. The contribution of the paper lies on our unifying technique that is applicable to various types of local and nonlocal operators.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
<a href="/cs/project/GA22-17403S" target="_blank" >GA22-17403S: Nelineární Schrödingerovy rovnice a systémy se singulárním potenciálem</a><br>
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Ostatní
Rok uplatnění
2023
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Acta Mathematica Vietnamica
ISSN
0251-4184
e-ISSN
2315-4144
Svazek periodika
48
Číslo periodika v rámci svazku
1
Stát vydavatele periodika
SG - Singapurská republika
Počet stran výsledku
26
Strana od-do
3-28
Kód UT WoS článku
000874131300001
EID výsledku v databázi Scopus
2-s2.0-85141029304