{"paper":{"title":"Schr\\\"odinger equations with singular potentials: linear and nonlinear boundary value problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Moshe Marcus, Phuoc-Tai Nguyen","submitted_at":"2018-03-12T12:07:39Z","abstract_excerpt":"Let $\\Omega \\subset {\\mathbb R}^N$ ($N \\geq 3$) be a $C^2$ bounded domain and $F \\subset \\partial \\Omega$ be a $C^2$ submanifold of dimension $0 \\leq k \\leq N-2$. Put $\\delta_F(x)=dist(x,F)$, $V=\\delta_F^{-2}$ in $\\Omega$ and $L_{\\gamma V}=\\Delta + \\gamma V$. Denote by $C_H(V)$ the Hardy constant relative to $V$ in $\\Omega$. We study positive solutions of equations (LE) $-L_{\\gamma V} u = 0$ and (NE) $-L_{\\gamma V} u+ f(u) = 0$ in $\\Omega$ when $\\gamma < C_H(V)$ and $f \\in C({\\mathbb R})$ is an odd, monotone increasing function. We establish the existence of a normalized boundary trace for pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04214","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":""},"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"}