{"paper":{"title":"Compactness and existence results in weighted Sobolev spaces of radial functions. Part II: Existence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marino Badiale, Michela Guida, Sergio Rolando","submitted_at":"2015-05-30T01:27:36Z","abstract_excerpt":"We prove existence and multiplicity results for finite energy solutions to the nonlinear elliptic equation \\[ -\\triangle u+V\\left( \\left| x\\right| \\right) u=g\\left( \\left| x\\right| ,u\\right) \\quad \\textrm{in }\\Omega \\subseteq \\mathbb{R}^{N},\\ N\\geq 3, \\] where $\\Omega $ is a radial domain (bounded or unbounded) and $u$ satisfies $u=0$ on $\\partial \\Omega $ if $\\Omega \\neq \\mathbb{R}^{N}$ and $u\\rightarrow 0$ as $\\left| x\\right| \\rightarrow \\infty $ if $\\Omega $ is unbounded. The potential $V$ may be vanishing or unbounded at zero or at infinity and the nonlinearity $g$ may be superlinear or su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00056","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"}