{"paper":{"title":"A fractional Kirchhoff problem involving a singular term and a critical nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Fiscella","submitted_at":"2017-03-22T21:24:09Z","abstract_excerpt":"In this paper we consider the following critical nonlocal problem $$ \\left\\{\\begin{array}{ll} M\\left(\\displaystyle\\iint_{\\mathbb{R}^{2N}}\\frac{|u(x)-u(y)|^2}{|x-y|^{N+2s}}dxdy\\right)(-\\Delta)^s u = \\displaystyle\\frac{\\lambda}{u^\\gamma}+u^{2^*_s-1}&\\quad\\mbox{in } \\Omega,\\\\ u>0&\\quad\\mbox{in } \\Omega,\\\\ u=0&\\quad\\mbox{in } \\mathbb{R}^N\\setminus\\Omega, \\end{array}\\right. $$ where $\\Omega$ is an open bounded subset of $\\mathbb R^N$ with continuous boundary, dimension $N>2s$ with parameter $s\\in (0,1)$, $2^*_s=2N/(N-2s)$ is the fractional critical Sobolev exponent, $\\lambda>0$ is a real parameter,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07861","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"}