{"paper":{"title":"Multiplicity results for fractional Laplace problems with critical growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Fiscella, Giovanni Molica Bisci, Raffaella Servadei","submitted_at":"2016-07-15T11:06:53Z","abstract_excerpt":"This paper deals with multiplicity and bifurcation results for nonlinear problems driven by the fractional Laplace operator $(-\\Delta)^s$ and involving a critical Sobolev term. In particular, we consider $$\\begin{cases} (-\\Delta)^su=\\gamma|u|^{2^*-2}u+f(x,u) & \\mbox{in } \\Omega u=0 & \\mbox{in } \\mathbb R^n\\setminus \\Omega, \\end{cases}$$ where $\\Omega\\subset\\mathbb R^n$ is an open bounded set with continuous boundary, $n>2s$ with $s\\in(0,1)$, $\\gamma$ is a positive real parameter, $2^*=2n/(n-2s)$ is the fractional critical Sobolev exponent and $f$ is a Carath\\'{e}odory function satisfying diffe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04462","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"}