{"paper":{"title":"Existence of nonradial positive and nodal solutions to a critical Neumann problem in a cone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filomena Pacella, M\\'onica Clapp","submitted_at":"2019-06-21T19:31:56Z","abstract_excerpt":"We study the critical Neumann problem \\begin{equation*} \\begin{cases} -\\Delta u = |u|^{2^*-2}u &\\text{in }\\Sigma_\\omega,\\\\ \\quad\\frac{\\partial u}{\\partial\\nu}=0 &\\text{on }\\partial\\Sigma_\\omega, \\end{cases} \\end{equation*} in the unbounded cone $\\Sigma_\\omega:=\\{tx:x\\in\\omega\\text{ and }t>0\\}$, where $\\omega$ is an open connected subset of the unit sphere $\\mathbb{S}^{N-1}$ in $\\mathbb{R}^N$ with smooth boundary, $N\\geq 3$ and $2^*:=\\frac{2N}{N-2}$. We assume that some local convexity condition at the boundary of the cone is satisfied.\n  If $\\omega$ is symmetric with respect to the north pole "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09301","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"}