{"paper":{"title":"Multiple solutions to a weakly coupled purely critical elliptic system in bounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jorge Faya, M\\'onica Clapp","submitted_at":"2018-05-25T18:05:22Z","abstract_excerpt":"We study the weakly coupled critical elliptic system \\begin{equation*} \\begin{cases} -\\Delta u=\\mu_{1}|u|^{2^{*}-2}u+\\lambda\\alpha |u|^{\\alpha-2}|v|^{\\beta}u & \\text{in }\\Omega,\\\\ -\\Delta v=\\mu_{2}|v|^{2^{*}-2}v+\\lambda\\beta |u|^{\\alpha}|v|^{\\beta-2}v & \\text{in }\\Omega,\\\\ u=v=0 & \\text{on }\\partial\\Omega, \\end{cases} \\end{equation*} where $\\Omega$ is a bounded smooth domain in $\\mathbb{R}^{N}$, $N\\geq 3$, $2^{*}:=\\frac{2N}{N-2}$ is the critical Sobolev exponent, $\\mu_{1},\\mu_{2}>0$, $\\alpha, \\beta>1$, $\\alpha+\\beta =2^{*}$ and $\\lambda\\in\\mathbb{R}$.\n  We establish the existence of a prescrib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10304","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"}