{"paper":{"title":"Positive ground states for a system of Schr\\\"odinger equations with critically growing nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jaros{\\l}aw Mederski, Pietro d'Avenia","submitted_at":"2014-03-13T09:34:34Z","abstract_excerpt":"We study the following problem \\[ \\begin{cases} -\\Delta u = \\lambda u + u^{2^*-2} v & \\hbox{in} \\Omega,\\\\ -\\Delta v= \\mu v^{2^*-1} + u^{2^*-1} & \\hbox{in} \\Omega,\\\\ u> 0,v> 0 & \\hbox{in} \\Omega,\\\\ u=v=0 & \\hbox{on} \\partial \\Omega, \\end{cases} \\] where $\\Omega$ is a bounded domain of $\\mathbb{R}^N$, $N\\geq 4$, $2^*=2N/(N-2)$, $\\lambda\\in\\mathbb{R}$ and $\\mu\\geq 0$ and we obtain existence and nonexistence results, depending on the value of the parameters $\\lambda$ and $\\mu$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3211","kind":"arxiv","version":3},"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"}