{"paper":{"title":"Doubly nonlocal system with Hardy-Littlewood-Sobolev critical nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"J.Giacomoni, K.Sreenadh, Tuhina Mukherjee","submitted_at":"2017-11-08T05:21:04Z","abstract_excerpt":"This article concerns about the existence and multiplicity of weak solutions for the following nonlinear doubly nonlocal problem with critical nonlinearity in the sense of Hardy-Littlewood-Sobolev inequality \\begin{equation*} \\left\\{ \\begin{split} (-\\Delta)^su &= \\lambda |u|^{q-2}u + \\left(\\int_{\\Omega}\\frac{|v(y)|^{2^*_\\mu}}{|x-y|^\\mu}~\\mathrm{d}y\\right) |u|^{2^*_\\mu-2}u\\; \\text{in}\\; \\Omega\n  (-\\Delta)^sv &= \\delta |v|^{q-2}v + \\left(\\int_{\\Om}\\frac{|u(y)|^{2^*_\\mu}}{|x-y|^\\mu}~\\mathrm{d}y \\right) |v|^{2^*_\\mu-2}v \\; \\text{in}\\; \\Omega\n  u &=v=0\\; \\text{in}\\; \\mb R^n\\setminus\\Omega, \\end{spl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02835","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"}