{"paper":{"title":"On Coron's problem for weakly coupled elliptic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Nicola Soave","submitted_at":"2016-10-25T07:39:29Z","abstract_excerpt":"We consider the following critical weakly coupled elliptic system \\[ \\begin{cases} -\\Delta u_i = \\mu_i |u_i|^{2^*-2}u_i + \\sum_{j \\neq i} \\beta_{ij} |u_j|^{\\frac{2^*}{2}} |u_i|^{\\frac{2^*-4}{2}} u_i & \\text{in $\\Omega_\\varepsilon$} u_i >0 & \\text{in $\\Omega_\\varepsilon$} u_i = 0 & \\text{on $\\partial \\Omega_\\varepsilon$},\\end{cases} \\qquad i =1,\\dots,m, \\] in a domain $\\Omega_\\varepsilon \\subset \\mathbb{R}^N$, $N=3,4$, with small shrinking holes as the parameter $\\varepsilon \\to 0$. We prove the existence of positive solutions of two different types: either each density concentrates around a di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07762","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"}