{"paper":{"title":"Nodal properties of eigenfunctions of a generalized buckling problem on balls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christophe Troestler, Colette De Coster, Serge Nicaise","submitted_at":"2014-08-26T16:33:16Z","abstract_excerpt":"In this paper we are interested in the following fourth order eigenvalue problem coming from the buckling of thin films on liquid substrates: \\begin{equation*}\n  \\begin{cases}\n  \\Delta^2 u+ \\kappa^2 u=-\\lambda \\Delta u &\\text{in } B_1,\\newline\n  u=\\partial_r u= 0 &\\text{on } \\partial B_1,\n  \\end{cases} \\end{equation*} where $B_1$ is the unit ball in $\\mathbb{R}^N$.\n  When $\\kappa > 0$ is small, we show that the first eigenvalue is simple and the first eigenfunction, which gives the shape of the film for small displacements, is positive. However, when $\\kappa$ increases, we establish that the f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6180","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"}