{"paper":{"title":"Decay properties of the Hardy-Littlewood-Sobolev systems of the Lane-Emden type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Congming Li, Yutian Lei","submitted_at":"2013-02-22T12:16:55Z","abstract_excerpt":"In this paper, we study the asymptotic behavior of positive solutions of the nonlinear differential systems of Lane-Emden type $2k$-order equations $$\\{{array}{l}\n  (-\\Delta)^k u=v^q,u>0 \\quad in ~R^n,\n  (-\\Delta)^k v=u^p,v>0 \\quad in ~R^n,\n  {array}. $$ and the Hardy-Littlewood-Sobolev (HLS) type system of nonlinear equations $$ \\{{array}{l} u(x)=\\displaystyle\\int_{R^n}\\frac{v^q(y)dy}{|x-y|^{n-\\alpha}},u>0 \\quad in ~R^n, v(x)=\\displaystyle\\int_{R^n}\\frac{u^p(y)dy}{|x-y|^{n-\\alpha}},u>0 \\quad in ~R^n.\n  {array}. $$ Such an integral system is related to the study the extremal functions of the H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5567","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"}