Publication details

Semilinear elliptic Schrödinger equations involving singular potentials and source terms

Investor logo

GKIKAS Konstantinos T NGUYEN Phuoc-Tai

Year of publication 2024
Type Article in Periodical
Magazine / Source Nonlinear Analysis
MU Faculty or unit

Faculty of Science

Keywords Hardy potentials; Critical exponents; Source terms; Capacities; Measure data
Description Let $?\subset \mathbb{R}^N$ ($N>2$) be a $C^2$ bounded domain and $?\subset ?$ be a compact, $C^2$ submanifold without boundary, of dimension $k$ with $0\leq k < N-2$. Put $L_µ= ?+ µd_?^{-2}$ in $?\setminus ?$, where $d_?(x) = \mathrm{dist}(x,?)$ and $µ$ is a parameter. We study the boundary value problem (P) $-L_µu = g(u) + ?$ in $?\setminus ?$ with condition $u=?$ on $\partial ?\cup ?$, where $g: \mathbb{R} \to \mathbb{R}$ is a nondecreasing, continuous function and $?$ and $?$ are positive measures. The interplay between the inverse-square potential $d_?^{-2}$, the nature of the source term $g(u)$ and the measure data $?,?$ 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.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.

More info