Semilinear elliptic Schrödinger equations involving singular
potentials and source terms

J 2024

Semilinear elliptic Schrödinger equations involving singular potentials and source terms

GKIKAS, Konstantinos T a Phuoc-Tai NGUYEN

Základní údaje

Originální název

Semilinear elliptic Schrödinger equations involving singular potentials and source terms

Autoři

GKIKAS, Konstantinos T a Phuoc-Tai NGUYEN (704 Vietnam, domácí)

Vydání

Nonlinear Analysis, Elsevier, 2024, 0362-546X

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Velká Británie a Severní Irsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.400 v roce 2022

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1016/j.na.2023.113403

UT WoS

001106766700001

Klíčová slova anglicky

Hardy potentials; Critical exponents; Source terms; Capacities; Measure data

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 25. 3. 2024 15:06, Mgr. Marie Šípková, DiS.

Anotace

V originále

Let $Ω\subset \mathbb{R}^N$ ($N>2$) be a $C^2$ bounded domain and $Σ\subset Ω$ be a compact, $C^2$ submanifold without boundary, of dimension $k$ with $0\leq k < N-2$. Put $L_μ= Δ+ μd_Σ^{-2}$ in $Ω\setminus Σ$, where $d_Σ(x) = \mathrm{dist}(x,Σ)$ and $μ$ is a parameter. We study the boundary value problem (P) $-L_μu = g(u) + τ$ in $Ω\setminus Σ$ with condition $u=ν$ on $\partial Ω\cup Σ$, where $g: \mathbb{R} \to \mathbb{R}$ is a nondecreasing, continuous function and $τ$ and $ν$ are positive measures. The interplay between the inverse-square potential $d_Σ^{-2}$, the nature of the source term $g(u)$ and the measure data $τ,ν$ yields substantial difficulties in the research of the problem. We perform a deep analysis based on delicate estimate on the Green kernel and Martin kernel and fine topologies induced by appropriate capacities to establish various necessary and sufficient conditions for the existence of a solution in different cases.

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

GKIKAS, Konstantinos T a Phuoc-Tai NGUYEN. Semilinear elliptic Schrödinger equations involving singular potentials and source terms. Nonlinear Analysis. Elsevier, 2024, roč. 238, January, s. 1-44. ISSN 0362-546X. Dostupné z: https://dx.doi.org/10.1016/j.na.2023.113403.

@article{2368112,
   author = {Gkikas, Konstantinos T and Nguyen, PhuocandTai},
   article_number = {January},
   doi = {http://dx.doi.org/10.1016/j.na.2023.113403},
   keywords = {Hardy potentials; Critical exponents; Source terms; Capacities; Measure data},
   language = {eng},
   issn = {0362-546X},
   journal = {Nonlinear Analysis},
   title = {Semilinear elliptic Schrödinger equations involving singular potentials and source terms},
   url = {https://www.sciencedirect.com/science/article/pii/S0362546X23001955},
   volume = {238},
   year = {2024}
}

TY  - JOUR
ID  - 2368112
AU  - Gkikas, Konstantinos T - Nguyen, Phuoc-Tai
PY  - 2024
TI  - Semilinear elliptic Schrödinger equations involving singular potentials and source terms
JF  - Nonlinear Analysis
VL  - 238
IS  - January
SP  - 1-44
EP  - 1-44
PB  - Elsevier
SN  - 0362546X
KW  - Hardy potentials
KW  - Critical exponents
KW  - Source terms
KW  - Capacities
KW  - Measure data
UR  - https://www.sciencedirect.com/science/article/pii/S0362546X23001955
N2  - Let $Ω\subset \mathbb{R}^N$ ($N>2$) be a $C^2$ bounded domain and $Σ\subset Ω$ be a compact, $C^2$ submanifold without boundary, of dimension $k$ with $0\leq k < N-2$. Put $L_μ= Δ+ μd_Σ^{-2}$ in $Ω\setminus Σ$, where $d_Σ(x) = \mathrm{dist}(x,Σ)$ and $μ$ is a parameter. We study the boundary value problem (P) $-L_μu = g(u) + τ$ in $Ω\setminus Σ$ with condition $u=ν$ on $\partial Ω\cup Σ$, where $g: \mathbb{R} \to \mathbb{R}$ is a nondecreasing, continuous function and $τ$ and $ν$ are positive measures. The interplay between the inverse-square potential $d_Σ^{-2}$, the nature of the source term $g(u)$ and the measure data $τ,ν$ yields substantial difficulties in the research of the problem. We perform a deep analysis based on delicate estimate on the Green kernel and Martin kernel and fine topologies induced by appropriate capacities to establish various necessary and sufficient conditions for the existence of a solution in different cases.
ER  -

GKIKAS, Konstantinos T a Phuoc-Tai NGUYEN. Semilinear elliptic Schrödinger equations involving singular potentials and source terms. \textit{Nonlinear Analysis}. Elsevier, 2024, roč.~238, January, s.~1-44. ISSN~0362-546X. Dostupné z: https://dx.doi.org/10.1016/j.na.2023.113403.

Podrobný výpis o publikaci