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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1507.01360","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-07-06T09:04:40Z","cross_cats_sorted":[],"title_canon_sha256":"5eccf06dfd0ea65920b944497f3fab4055474f14d675ca0b608edfbf227a82f7","abstract_canon_sha256":"8489193b46ca9fe172a037648677fb09fe338bca9f5adc2ba4a5086467f2dd7b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:01.619893Z","signature_b64":"RgQsrdpgKWdabNnTH1tGLlP57dyA5CJMv9yyT6GL7zLwkJMx90nH1jQEnyV+jMMhCydXHXqm3YcZ24h1esKeCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0edca248ae42e1d7c3e90b8df300e40410ccd610e6e3cdfeed9413a6c74c37f2","last_reissued_at":"2026-05-18T01:20:01.619193Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:01.619193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $N\\geq3$. 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