{"paper":{"title":"Existence and symmetry of positive ground states for a doubly critical Schrodinger system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wenming Zou, Zhijie Chen","submitted_at":"2012-11-07T11:11:13Z","abstract_excerpt":"We study the following doubly critical Schr\\\"{o}dinger system $$-\\Delta u -\\frac{\\la_1}{|x|^2}u=u^{2^\\ast-1}+ \\nu \\al u^{\\al-1}v^\\bb, \\quad x\\in \\RN, -\\Delta v -\\frac{\\la_2}{|x|^2}v=v^{2^\\ast-1} + \\nu \\bb u^{\\al}v^{\\bb-1}, \\quad x\\in \\RN, u, v\\in D^{1, 2}(\\RN),\\quad u, v>0 in $\\RN\\setminus{0}$},$$ where $N\\ge 3$, $\\la_1, \\la_2\\in (0, \\frac{(N-2)^2}{4})$, $2^\\ast=\\frac{2N}{N-2}$ and $\\al>1, \\bb>1$ satisfying $\\al+\\bb=2^\\ast$. This problem is related to coupled nonlinear Schr\\\"{o}dinger equations with critical exponent for Bose-Einstein condensate. For different ranges of $N$, $\\al$, $\\bb$ and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1514","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"}