{"paper":{"title":"Sign-changing blowing-up solutions for supercritical Bahri-Coron's problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Monica Musso","submitted_at":"2015-02-05T18:43:20Z","abstract_excerpt":"Let $\\Omega$ be a bounded domain in $\\R^n$, $n\\ge 3$ with smooth boundary $\\partial\\Omega$ and a small hole. We give the first example of sign-changing {\\it bubbling} solutions to the nonlinear elliptic problem $$\n  -\\Delta u=|u|^{{n+2\\over n-2} +\\ve -1 } u \\, \\, \\mbox{ in } \\Omega , \\quad \\quad\n  u=0 \\mbox{ on } \\partial \\Omega, $$ where $\\ve$ is a small positive parameter. The basic cell in the construction is the sign-changing nodal solution to the critical Yamabe problem $$ -\\Delta w = |w|^{\\frac{4}{n-2}} w, \\ \\ w \\in {\\mathcal D}^{1,2} (\\R^n) $$ which has large number ($3n$) of kernels."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01674","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"}