{"paper":{"title":"Infinitely many non-radial solutions to a critical equation on annulus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Benniao Li, Shusen Yan, Yuxia Guo","submitted_at":"2018-04-05T06:55:47Z","abstract_excerpt":"In this paper, we build infinitely many non-radial sign-changing solutions to the critical problem: \\begin{equation*} \\left\\{\\begin{array}{rlll} -\\Delta u&=|u|^{\\frac{4}{N-2}}u, &\\hbox{ in }\\Omega,\\\\ u&=0, &\\hbox{ on }\\partial\\Omega. \\end{array}\\right. \\eqno(P) \\end{equation*} on the annulus $\\Omega:=\\{x\\in \\mathbb{R}^N: a<|x|<b\\}$, $N\\geq 3.$ In particular, for any integer $k$ large enough, we build a non-radial solution which look like the unique positive solution $u_0$ to $(P)$ crowned by $k$ negative bubbles arranged on a regular polygon with radius $r_0$ such that $r_0^{\\frac{N-2}{2}}u_0("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01687","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"}