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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 "},"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":"1406.3970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-16T11:02:10Z","cross_cats_sorted":[],"title_canon_sha256":"b65c998282415bfe7bb4648937a9bba01ea5aef9f64139b5843c36247dbcbd58","abstract_canon_sha256":"42eafee97a93a38a5e3806782e10ee5f01eeabc35028099f039120847ca37278"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:48.869389Z","signature_b64":"wfrNnfW70UbpCe0I3CXGNDy0OtIFNZt6LwU4wbXkdWwdKFC++rl+k2aZCdmT32BJDg45iGTvFfR2hZXy40VyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b5d607fb315abe18f9878154d7ed585dbdd235ed5f408382c4779e74559a30f","last_reissued_at":"2026-05-18T01:22:48.868675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:48.868675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $p\\to+\\infty$. 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