{"paper":{"title":"A critical nonlinear fractional elliptic equation with saddle-like potentical in $\\mathbb{R}^N$","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":"2015-06-22T10:06:58Z","abstract_excerpt":"In this paper, we study the existence of positive solution for the following class of fractional elliptic equation $$ \\epsilon^{2s} (-\\Delta)^{s}{u}+V(z)u=\\lambda |u|^{q-2}u+|u|^{2^{*}_{s}-2}u\\,\\,\\, \\mbox{in} \\,\\,\\, \\mathbb{R}^{N}, $$ where $\\epsilon, \\lambda >0$ are positive parameters, $q \\in (2,2^{*}_{s}), 2^{*}_{s}=\\frac{2N}{N-2s}, $ $N > 2s,$ $s \\in (0,1),$ $ (-\\Delta)^{s}u$ is the fractional laplacian, and $V$ is a saddle-like potential. The result is proved by using minimizing method constrained to the Nehari manifold. A special minimax level is obtained by using an argument made by Ben"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06533","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"}