{"paper":{"title":"A nonexistence result for sign-changing solutions of the Brezis-Nirenberg problem in low dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Iacopetti, Filomena Pacella","submitted_at":"2014-06-30T11:40:51Z","abstract_excerpt":"We consider the Brezis-Nirenberg problem: \\begin{equation*} \\begin{cases} -\\Delta u = \\lambda u + |u|^{2^* -2}u & \\hbox{in}\\ \\Omega\\\\ u=0 & \\hbox{on}\\ \\partial \\Omega, \\end{cases} \\end{equation*} where $\\Omega$ is a smooth bounded domain in $\\mathbb{R}^N$, $N\\geq 3$, $2^{*}=\\frac{2N}{N-2}$ is the critical Sobolev exponent and $\\lambda>0$ a positive parameter.\n  The main result of the paper shows that if $N=4,5,6$ and $\\lambda$ is close to zero there are no sign-changing solutions of the form $$u_\\lambda=PU_{\\delta_1,\\xi}-PU_{\\delta_2,\\xi}+w_\\lambda, $$ where $PU_{\\delta_i}$ is the projection o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7681","kind":"arxiv","version":2},"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"}