{"paper":{"title":"Quasi-radial nodal solutions for the Lane-Emden problem in the ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesca Gladiali, Isabella Ianni","submitted_at":"2017-09-11T10:03:25Z","abstract_excerpt":"We consider the semilinear elliptic problem \\begin{equation}\\label{problemAbstract} \\left\\{\\begin{array}{lr}-\\Delta u= |u|^{p-1}u\\qquad \\mbox{ in }B\\\\ u=0\\qquad\\qquad\\qquad\\mbox{ on }\\partial B \\end{array}\\right.\\tag{$\\mathcal E_p$} \\end{equation} where $B$ is the unit ball of $\\mathbb R^2$ centered at the origin and $p\\in (1,+\\infty)$. We prove the existence of non-radial sign-changing solutions to \\eqref{problemAbstract} which are \\emph{quasi-radial}, namely solutions whose nodal line is the union of a finite number of disjoint simple closed curves, which are the boundary of nested domains c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03315","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"}