{"paper":{"title":"A Morse index formula for 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":"2016-05-11T09:58:41Z","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 $\\mathbb R^N$, $N\\geq3$, centered at the origin and $1<p<p_S$, $p_S=\\frac{N+2}{N-2}$. We prove that for any radial solution $u_p$ of \\eqref{problemAbstract} with $m$ nodal domains its Morse index $\\mathsf{m}(u_p)$ is given by the formula \\[\\mathsf{m}(u_p)=m+N(m-1)\\] if $p$ is sufficiently close to $p_S$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03357","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"}