Compactness of Green operators with applications to semilinear
nonlocal elliptic equations

J 2025

Compactness of Green operators with applications to semilinear nonlocal elliptic equations

HUYNH, Phuoc-Truong a Phuoc-Tai NGUYEN

Základní údaje

Originální název

Compactness of Green operators with applications to semilinear nonlocal elliptic equations

Autoři

HUYNH, Phuoc-Truong a Phuoc-Tai NGUYEN

Vydání

Journal of Differential Equations, Academic Press Inc. 2025, 0022-0396

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 2.300 v roce 2024

Označené pro přenos do RIV

Ano

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Integro-differential operators; Compactness; Green function; Kato-type inequalities; Critical exponents; Weak-dual solutions

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 7. 1. 2025 14:32, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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>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.

Návaznosti

GA22-17403S, projekt VaV

Název: Nelineární Schrödingerovy rovnice a systémy se singulárním potenciálem (Akronym: NSESSP)

Investor: Grantová agentura ČR, Nonlinear Schrödinger equations and systems with singular potentials

Citovat

HUYNH, Phuoc-Truong a Phuoc-Tai NGUYEN. Compactness of Green operators with applications to semilinear nonlocal elliptic equations. Journal of Differential Equations. Academic Press Inc., 2025, roč. 418, February, s. 97-141. ISSN 0022-0396. Dostupné z: https://doi.org/10.1016/j.jde.2024.11.019.

@article{2465626,
   author = {Huynh, PhuocandTruong and Nguyen, PhuocandTai},
   article_number = {February},
   doi = {https://doi.org/10.1016/j.jde.2024.11.019},
   keywords = {Integro-differential operators; Compactness; Green function; Kato-type inequalities; Critical exponents; Weak-dual solutions},
   language = {eng},
   issn = {0022-0396},
   journal = {Journal of Differential Equations},
   title = {Compactness of Green operators with applications to semilinear nonlocal elliptic equations},
   url = {https://www.sciencedirect.com/science/article/pii/S0022039624007356},
   volume = {418},
   year = {2025}
}

TY  - JOUR
ID  - 2465626
AU  - Huynh, Phuoc-Truong - Nguyen, Phuoc-Tai
PY  - 2025
TI  - Compactness of Green operators with applications to semilinear nonlocal elliptic equations
JF  - Journal of Differential Equations
VL  - 418
IS  - February
SP  - 97-141
EP  - 97-141
PB  - Academic Press Inc.
SN  - 00220396
KW  - Integro-differential operators
KW  - Compactness
KW  - Green function
KW  - Kato-type inequalities
KW  - Critical exponents
KW  - Weak-dual solutions
UR  - https://www.sciencedirect.com/science/article/pii/S0022039624007356
N2  - 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>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.
ER  -

HUYNH, Phuoc-Truong a Phuoc-Tai NGUYEN. Compactness of Green operators with applications to semilinear nonlocal elliptic equations. \textit{Journal of Differential Equations}. Academic Press Inc., 2025, roč.~418, February, s.~97-141. ISSN~0022-0396. Dostupné z: https://doi.org/10.1016/j.jde.2024.11.019.

Přehled o publikaci