{"paper":{"title":"A Liouville type theorem for Lane-Emden systems involving the fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Quaas, Aliang Xia","submitted_at":"2015-11-07T12:01:42Z","abstract_excerpt":"We establish a Liouville type theorem for the fractional Lane-Emden system:\n  \\begin{eqnarray*} \\left\\{\\begin{array}{l@{\\quad }l} (-\\Delta)^\\alpha u=v^q&{\\rm in}\\,\\,\\R^N,\\\\ (-\\Delta)^\\alpha v=u^p&{\\rm in}\\,\\,\\R^N,\n  \\end{array}\n  \\right.\n  \\end{eqnarray*}\n  where $ \\alpha\\in(0,1) $, $ N>2\\alpha $ and $ p,q $ are positive real numbers and in an appropriate new range.\n  To prove our result we will use the local realization of fractional Laplacian, which can be constructed as Dirichlet-to-Neumann operator of a degenerate elliptic equation in the spirit of Caffarelli and Silvestre \\cite{CS}. Our p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02346","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"}