{"paper":{"title":"Existence, nonexistence, symmetry and uniqueness of ground state for critical Schr\\\"odinger system involving Hardy term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Senping Luo, Wenming Zou","submitted_at":"2016-08-03T09:10:21Z","abstract_excerpt":"We study the following elliptic system with critical exponent: \\begin{displaymath} \\begin{cases}-\\Delta u_j-\\frac{\\lambda_j}{|x|^2}u_j=u_j^{2^*-1}+\\sum\\limits_{k\\neq j}\\beta_{jk}\\alpha_{jk}u_j^{\\alpha_{jk}-1}u_k^{\\alpha_{kj}},\\;\\;x\\in\\R^N, u_j\\in D^{1,2}(\\R^N),\\quad u_j>0 \\;\\; \\hbox{in} \\quad \\R^N\\setminus \\{0\\},\\quad j=1,...,r.\\end{cases}\\end{displaymath} Here $N\\geq 3, r\\geq2, 2^*=\\frac{2N}{N-2}, \\lambda_j\\in (0, \\frac{(N-2)^2}{4})$ for all $ j=1,...,r $; $\\beta_{jk}=\\beta_{kj}$; \\; $\\alpha_{jk}>1, \\alpha_{kj}>1,$ satisfying $\\alpha_{jk}+\\alpha_{kj}=2^* $ for all $k\\neq j$. Note that the non"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01123","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"}