{"paper":{"title":"A fountain of positive Bubbles on a Coron's Problem for a Competitive Weakly Coupled Gradient System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Hugo Tavares, Nicola Soave","submitted_at":"2018-12-11T09:14:57Z","abstract_excerpt":"We consider the following critical elliptic system: \\begin{equation*} \\begin{cases} -\\Delta u_i=\\mu_i u_i^{3}+\\beta u_i^{ } \\sum\\limits_{j\\neq i} u_j^{2} \\quad \\hbox{in}\\ \\Omega_\\varepsilon \\\\ u_i=0 \\hbox{ on } \\partial\\Omega_\\varepsilon , \\qquad u_i>0 \\hbox{ in } \\Omega_\\varepsilon \\end{cases}\\qquad i=1,\\ldots, m, \\end{equation*} in a domain $\\Omega_\\varepsilon \\subset \\mathbb{R}^4$ with a small shrinking hole $B_\\varepsilon(\\xi_0)$. For $\\mu_i>0$, $\\beta<0$, and $\\varepsilon>0$ small, we prove the existence of a non-synchronized solution which looks like a fountain of positive bubbles, i.e. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04280","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"}