{"paper":{"title":"A Pohozaev Identity for the Fractional H$\\acute{e}$non System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fengquan Li, Pei Ma, Yan Li","submitted_at":"2016-04-27T22:02:40Z","abstract_excerpt":"In this paper, we study the Pohozaev identity associated with a H$\\acute{e}$non-Lane-Emden system involving the fractional Laplacian:\n  \\begin{equation}\n  \\left\\{\\begin{array}{ll}\n  (-\\triangle)^su=|x|^av^p,&x\\in\\Omega,\n  (-\\triangle)^sv=|x|^bu^q,&x\\in\\Omega, u=v=0,&x\\in R^n\\backslash\\Omega,\n  \\end{array}\n  \\right.\n  \\end{equation} in a star-shaped and bounded domain $\\Omega$ for $s\\in(0,1)$. As an application of our identity, we deduce the nonexistence of positive solutions in the critical and supercritical cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08258","kind":"arxiv","version":2},"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"}