{"paper":{"title":"Classification of Solutions to a Critically Nonlinear System of Elliptic Equations on Euclidean Half-Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lei Zhang, Mathew R. Gluck","submitted_at":"2014-01-12T20:32:48Z","abstract_excerpt":"For $N\\geq 3$ and non-negative real numbers $a_{ij}$ and $b_{ij}$ ($i,j= 1, \\cdots, m$), the semi-linear elliptic system\n  \\begin{equation*}\n  \\begin{cases}\n  \\Delta u_i + \\prod_{j = 1}^m u_j^{a_{ij}} = 0\n  &\n  \\text{ in } \\mathbb R_+^N,\n  \\frac{\\partial u_i}{\\partial y_N}\n  = c_i \\prod_{j = 1}^m u_j^{b_{ij}}\n  &\n  \\text{ on } \\partial \\mathbb R_+^N\n  \\end{cases}\n  \\qquad i = 1, \\cdots, m \\end{equation*} %\nis considered, where $\\mathbb R_+^N$ is the upper half of $N$-dimensional Euclidean space. Under suitable assumptions on the exponents $a_{ij}$ and $b_{ij}$, a classification theorem for the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2666","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"}