{"paper":{"title":"Sign-changing blowing-up solutions for the Brezis--Nirenberg problem in dimensions four and five","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Iacopetti, Giusi Vaira","submitted_at":"2015-04-20T10:53:45Z","abstract_excerpt":"We consider the Brezis-Nirenberg problem: $$-\\Delta u =\\lambda u + |u|^{p-1}u\\qquad \\mbox{in}\\,\\, \\Omega,\\quad u=0\\,\\, \\mbox{on}\\,\\,\\ \\partial\\Omega,$$ where $\\Omega$ is a smooth bounded domain in $\\mathbb R^N$, $N\\geq 3$, $p=\\frac{N+2}{N-2}$ and $\\lambda>0$. In this paper we prove that, if $\\Omega$ is symmetric and $N=4,5$, there exists a sign-changing solution whose positive part concentrates and blows-up at the center of symmetry of the domain, while the negative part vanishes, as $\\lambda\\rightarrow \\lambda_1$, where $\\lambda_1=\\lambda_1(\\Omega)$ denotes the first eigenvalue of $-\\Delta$ o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05010","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"}