{"paper":{"title":"Positive Least Energy Solutions and Phase Separation for Coupled Schrodinger Equations with Critical Exponent: Higher Dimensional Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wenming Zou, Zhijie Chen","submitted_at":"2012-09-12T08:47:12Z","abstract_excerpt":"We study the following nonlinear Schr\\\"{o}dinger system which is related to Bose-Einstein condensate: {displaymath} {cases}-\\Delta u +\\la_1 u = \\mu_1 u^{2^\\ast-1}+\\beta u^{\\frac{2^\\ast}{2}-1}v^{\\frac{2^\\ast}{2}}, \\quad x\\in \\Omega, -\\Delta v +\\la_2 v =\\mu_2 v^{2^\\ast-1}+\\beta v^{\\frac{2^\\ast}{2}-1} u^{\\frac{2^\\ast}{2}}, \\quad x\\in \\om, u\\ge 0, v\\ge 0 \\,\\,\\hbox{in $\\om$},\\quad u=v=0 \\,\\,\\hbox{on $\\partial\\om$}.{cases}{displaymath} Here $\\om\\subset \\R^N$ is a smooth bounded domain, $2^\\ast:=\\frac{2N}{N-2}$ is the Sobolev critical exponent, $-\\la_1(\\om)<\\la_1,\\la_2<0$, $\\mu_1,\\mu_2>0$ and $\\beta\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2522","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"}