{"paper":{"title":"Existence and concentration of solution for a class of fractional elliptic equation in $\\mathbb{R}^N$ via penalization method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudianor O. Alves, Olimpio H. Miyagaki","submitted_at":"2015-08-17T10:04:41Z","abstract_excerpt":"In this paper, we study the existence and concentration of positive solution for the following class of fractional elliptic equation $$ \\epsilon^{2s} (-\\Delta)^{s}{u}+V(z)u=f(u)\\,\\,\\, \\mbox{in} \\,\\,\\, \\mathbb{R}^{N}, $$ where $\\epsilon$ is a positive parameter, $f$ has a subcritical growth, $V$ possesses a local minimum, $N > 2s,$ $s \\in (0,1),$ and $ (-\\Delta)^{s}u$ is the fractional laplacian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03964","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"}