{"paper":{"title":"A critical fractional equation with concave-convex power nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"B. Barrios, E. Colorado, F. Soria, R. Servadei","submitted_at":"2013-06-13T18:39:34Z","abstract_excerpt":"In this work we study the following fractional critical problem $$ (P_{\\lambda})=\\left\\{\\begin{array}{ll} (-\\Delta)^s u=\\lambda u^{q} + u^{2^*_{s}-1}, \\quad u{>}0 & \\mbox{in} \\Omega\\\\ u=0 & \\mbox{in} \\RR^n\\setminus \\Omega\\,, \\end{array}\\right. $$ where $\\Omega\\subset \\mathbb{R}^n$ is a regular bounded domain, $\\lambda>0$, $0<s<1$ and $n>2s$. Here $(-\\Delta)^s$ denotes the fractional Laplace operator defined, up to a normalization factor, by $$ -(-\\Delta)^s u(x)={\\rm P. V.} \\int_{\\RR^n}\\frac{u(x+y)+u(x-y)-2u(x)}{|y|^{n+2s}}\\,dy, \\quad x\\in \\RR^n. $$ Our main results show the existence and multi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3190","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"}