{"paper":{"title":"On the Brezis-Nirenberg type critical problem for nonlinear Choquard equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fashun Gao, Minbo Yang","submitted_at":"2016-04-04T11:53:44Z","abstract_excerpt":"We establish some existence results for the Brezis-Nirenberg type problem of the nonlinear Choquard equation $$-\\Delta u =\\left(\\int_{\\Omega}\\frac{|u|^{2_{\\mu}^{\\ast}}}{|x-y|^{\\mu}}dy\\right)|u|^{2_{\\mu}^{\\ast}-2}u+\\lambda u\\4.14mm\\mbox{in}\\1.14mm \\Omega, $$ where $\\Omega$ is a bounded domain of $\\mathbb{R}^N$, with Lipschitz boundary, $\\lambda$ is a real parameter, $N\\geq3$, $2_{\\mu}^{\\ast}=(2N-\\mu)/(N-2)$ is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00826","kind":"arxiv","version":4},"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"}