{"paper":{"title":"Semilinear elliptic Schr\\\"odinger equations with singular potentials and absorption terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Konstantinos T. Gkikas, Phuoc-Tai Nguyen","submitted_at":"2022-03-02T17:48:15Z","abstract_excerpt":"Let $\\Omega \\subset \\mathbb{R}^N$ ($N \\geq 3$) be a $C^2$ bounded domain and $\\Sigma \\subset \\Omega$ be a compact, $C^2$ submanifold without boundary, of dimension $k$ with $0\\leq k < N-2$. Put $L_\\mu = \\Delta + \\mu d_\\Sigma^{-2}$ in $\\Omega \\setminus \\Sigma$, where $d_\\Sigma(x) = \\mathrm{dist}(x,\\Sigma)$ and $\\mu$ is a parameter. We investigate the boundary value problem (P) $-L_\\mu u + g(u) = \\tau$ in $\\Omega \\setminus \\Sigma$ with condition $u=\\nu$ on $\\partial \\Omega \\cup \\Sigma$, where $g: \\mathbb{R} \\to \\mathbb{R}$ is a nondecreasing, continuous function, and $\\tau$ and $\\nu$ are positiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.01266","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.01266/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}