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 and Phuoc-Tai NGUYEN

Basic information

Original name

Semilinear elliptic Schrödinger equations involving singular potentials and source terms

Authors

GKIKAS, Konstantinos T and Phuoc-Tai NGUYEN (704 Viet Nam, belonging to the institution)

Edition

Nonlinear Analysis, Elsevier, 2024, 0362-546X

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United Kingdom of Great Britain and Northern Ireland

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 1.400 in 2022

Organization unit

Faculty of Science

DOI

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

UT WoS

001106766700001

Keywords in English

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

Abstract

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.

Links

GA22-17403S, research and development project

Name: Nelineární Schrödingerovy rovnice a systémy se singulárním potenciálem (Acronym: NSESSP)

Investor: Czech Science Foundation

Citovat

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

Detailed Information on Publication Record