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@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.
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