{"paper":{"title":"On the structure of the second eigenfunctions of the p-Laplacian on a ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"P. Drabek, Sarath Sasi, T. V. Anoop","submitted_at":"2015-06-17T02:05:43Z","abstract_excerpt":"In this paper, we prove that the second eigenfunctions of the $p$-Laplacian, $p>1$, are not radial on the unit ball in $\\mathbb{R}^N,$ for any $N\\ge 2.$ Our proof relies on the variational characterization of the second eigenvalue and a variant of the deformation lemma. We also construct an infinite sequence of eigenpairs $\\{\\tau_n,\\Psi_n\\}$ such that $\\Psi_n$ is nonradial and has exactly $2n$ nodal domains. A few related open problems are also stated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05184","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"}