{"paper":{"title":"Morse index and sign changing bubble towers for Lane-Emden problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filomena Pacella, Francesca De Marchis, Isabella Ianni","submitted_at":"2014-06-16T11:02:10Z","abstract_excerpt":"We consider the semilinear Lane-Emden problem \\begin{equation}\\label{problemAbstract}\\left\\{ \\begin{array}{lr} -\\Delta u= |u|^{p-1}u\\qquad \\mbox{ in }\\Omega\\\\ u=0\\qquad\\qquad\\qquad\\mbox{ on }\\partial \\Omega \\end{array} \\right.\\tag{$\\mathcal E_p$} \\end{equation} where $p>1$ and $\\Omega$ is a smooth bounded symmetric domain of $\\mathbb R^2$. We show that for families $(u_p)$ of sign-changing symmetric solutions of \\eqref{problemAbstract} an upper bound on their Morse index implies concentration of the positive and negative part, $u_p^\\pm$, at the same point, as $p\\to+\\infty$. Then an asymptotic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3970","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"}