{"paper":{"title":"Positive solutions of semilinear elliptic problems with a Hardy potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Catherine Bandle, Maria Assunta Pozio","submitted_at":"2018-03-22T15:10:14Z","abstract_excerpt":"Let $\\Omega \\subset \\mathbb{R}^N$ be a bounded domain and $\\delta(x)$ be the distance of a point $x\\in \\Omega$ to the boundary. We study the positive solutions of the problem $\\Delta u +\\frac{\\mu}{\\delta(x)^2}u=u^p$ in $\\Omega$, where $p>0, \\,p\\ne 1$ and $\\mu \\in \\mathbb{R},\\,\\mu\\ne 0$ is smaller then the Hardy constant. The interplay between the singular potential and the nonlinearity leads to interesting structures of the solution sets. In this paper we first give the complete picture of the radial solutions in balls. In particular we establish for $p>1$ the existence of a unique large solut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08397","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"}