{"paper":{"title":"Fractional elliptic problems with critical growth in the whole of $\\R^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enrico Valdinoci, Maria Medina, Serena Dipierro","submitted_at":"2015-06-04T23:20:25Z","abstract_excerpt":"We study the following nonlinear and nonlocal elliptic equation in~$\\R^n$ $$ (-\\Delta)^s u = \\epsilon\\,h\\,u^q + u^p \\ {\\mbox{ in }}\\R^n, $$ where~$s\\in(0,1)$, $n>2s$, $\\epsilon>0$ is a small parameter, $p=\\frac{n+2s}{n-2s}$, $q\\in(0,1)$, and~$h\\in L^1(\\R^n)\\cap L^\\infty(\\R^n)$. The problem has a variational structure, and this allows us to find a positive solution by looking at critical points of a suitable energy functional. In particular, in this paper, we find a local minimum and a mountain pass solution of this functional. One of the crucial ingredient is a Concentration-Compactness princi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01748","kind":"arxiv","version":2},"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"}