{"paper":{"title":"Exact Morse index computation for nodal radial solutions of 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":"2015-07-06T09:04:40Z","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 }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 $\\mathbb R^N$, $N\\geq2$, centered at the origin and $1<p<p_S$, with $p_S=+\\infty$ if $N=2$ and $p_S=\\frac{N+2}{N-2}$ if $N\\geq3$. Our main result is to prove that in dimension $N=2$ the Morse index of the least energy sign-changing radial solution $u_p$ of \\eqref{problemAbstract} is exactly $12$ if $p$ is sufficiently la"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01360","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"}