{"paper":{"title":"Solutions of semilinear elliptic equations in tubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Berardino Sciunzi, Filomena Pacella, Frank Pacard","submitted_at":"2012-10-05T10:50:07Z","abstract_excerpt":"Given a smooth compact k-dimensional manifold \\Lambda embedded in $\\mathbb {R}^m$, with m\\geq 2 and 1\\leq k\\leq m-1, and given \\epsilon>0, we define B_\\epsilon (\\Lambda) to be the geodesic tubular neighborhood of radius \\epsilon about \\Lambda.\n  In this paper, we construct positive solutions of the semilinear elliptic equation \\Delta u + u^p = 0 in B_\\epsilon (\\Lambda) with u = 0 on \\partial B_\\epsilon (\\Lambda), when the parameter \\epsilon is chosen small enough. In this equation, the exponent p satisfies either p > 1 when n:=m-k \\leq 2 or p\\in (1, \\frac{n+2}{n-2}) when n>2. In particular p c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1705","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"}