Compactness of Green operators with applications to semilinear nonlocal elliptic equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F25%3A00144250" target="_blank" >RIV/00216224:14310/25:00144250 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0022039624007356" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022039624007356</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2024.11.019" target="_blank" >10.1016/j.jde.2024.11.019</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Compactness of Green operators with applications to semilinear nonlocal elliptic equations

Popis výsledku v původním jazyce

In this paper, we consider a class of integro-differential operators L posed on a C2 bounded domain Ω⊂RN with appropriate homogeneous Dirichlet conditions where each of which admits an inverse operator commonly known as the Green operator GΩ. Under mild conditions on L and its Green operator, we establish various sharp compactness of GΩ involving weighted Lebesgue spaces and weighted measure spaces. These results are then employed to prove the solvability for semilinear elliptic equation Lu+g(u)=μ in Ω with boundary condition u=0 on ∂Ω or exterior condition u=0 in RN∖Ω if applicable, where μ is a Radon measure on Ω and g:R→R is a nondecreasing continuous function satisfying a subcriticality integral condition. When g(t)=|t|p-1t with p&gt;1, we provide a sharp sufficient condition expressed in terms of suitable Bessel capacities for the existence of a solution. The contribution of the paper consists of (i) developing novel unified techniques which allow to treat various types of fractional operators and (ii) obtaining sharp compactness and existence results in weighted spaces, which refine and extend several related results in the literature.

Název v anglickém jazyce

Compactness of Green operators with applications to semilinear nonlocal elliptic equations

Popis výsledku anglicky

In this paper, we consider a class of integro-differential operators L posed on a C2 bounded domain Ω⊂RN with appropriate homogeneous Dirichlet conditions where each of which admits an inverse operator commonly known as the Green operator GΩ. Under mild conditions on L and its Green operator, we establish various sharp compactness of GΩ involving weighted Lebesgue spaces and weighted measure spaces. These results are then employed to prove the solvability for semilinear elliptic equation Lu+g(u)=μ in Ω with boundary condition u=0 on ∂Ω or exterior condition u=0 in RN∖Ω if applicable, where μ is a Radon measure on Ω and g:R→R is a nondecreasing continuous function satisfying a subcriticality integral condition. When g(t)=|t|p-1t with p&gt;1, we provide a sharp sufficient condition expressed in terms of suitable Bessel capacities for the existence of a solution. The contribution of the paper consists of (i) developing novel unified techniques which allow to treat various types of fractional operators and (ii) obtaining sharp compactness and existence results in weighted spaces, which refine and extend several related results in the literature.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

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)

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

1090-2732

Svazek periodika

418

Číslo periodika v rámci svazku

February

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

45

Strana od-do

97-141

Kód UT WoS článku

001364125100001

EID výsledku v databázi Scopus

2-s2.0-85209567326