Semilinear elliptic Schrödinger equations involving singular potentials and source terms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F24%3A00139355" target="_blank" >RIV/00216224:14310/24:00139355 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0362546X23001955" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0362546X23001955</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.na.2023.113403" target="_blank" >10.1016/j.na.2023.113403</a>

Result language
angličtina
Original language name
Semilinear elliptic Schrödinger equations involving singular potentials and source terms
Original language description
Let $Ωsubset mathbb{R}^N$ ($N>2$) be a $C^2$ bounded domain and $Σsubset Ω$ be a compact, $C^2$ submanifold without boundary, of dimension $k$ with $0leq k < N-2$. Put $L_μ= Δ+ μd_Σ^{-2}$ in $Ωsetminus Σ$, 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 $Ωsetminus Σ$ with condition $u=ν$ on $partial Ωcup Σ$, 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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA22-17403S" target="_blank" >GA22-17403S: Nonlinear Schrödinger equations and systems with singular potentials</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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