{"paper":{"title":"Existence, unique continuation and symmetry of least energy nodal solutions to sublinear Neumann problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enea Parini, Tobias Weth","submitted_at":"2014-01-28T13:56:40Z","abstract_excerpt":"We consider the sublinear problem \\begin {equation*} \\left\\{\\begin{array}{r c l c} -\\Delta u & = &|u|^{q-2}u & \\textrm{in }\\Omega, \\\\ u_n & = & 0 & \\textrm{on }\\partial\\Omega,\\end{array}\\right. \\end {equation*} where $\\Omega \\subset \\real^N$ is a bounded domain, and $1 \\leq q < 2$. For $q=1$, $|u|^{q-2}u$ will be identified with $\\sgn(u)$. We establish a variational principle for least energy nodal solutions, and we investigate their qualitative properties. In particular, we show that they satisfy a unique continuation property (their zero set is Lebesgue-negligible). Moreover, if $\\Omega$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7182","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"}