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We address the question of estimating the Morse index $m(u)$ of a sign changing radial solution $u$. We prove that $m(u) \\geq 3$ for every $\\alpha>0$ and that $m(u)\\geq \\alpha+ 3$ if $\\alpha$ is even. If $f$ is superlinear the pr"},"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":"1503.02999","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-10T17:32:45Z","cross_cats_sorted":[],"title_canon_sha256":"ba912286647ad664982c0f45b4f255a6a352c4029dd3028bfbf36226f8dc60b9","abstract_canon_sha256":"08120bd6f0190f0909c46b31f46daeb1f004bc2c9ba877c37e6832faa4a41d80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:25.396504Z","signature_b64":"NBIPLDXziAbVRsmwSL4ospPPYMneuAUusztljGzadWs6vC4E5d2Gx5LJoSD6l1ueeMnXDXWyqzNFuu3tQLaXAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58aacef6726ee427b73a056f384f776f98cf041c86de424518ba36c002168c37","last_reissued_at":"2026-05-18T01:11:25.395989Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:25.395989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Morse index of radial nodal solutions of H\\'enon type equations in dimension two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ederson Moreira dos Santos, Filomena Pacella","submitted_at":"2015-03-10T17:32:45Z","abstract_excerpt":"We consider non-autonomous semilinear elliptic equations of the type \\[ -\\Delta u = |x|^{\\alpha} f(u), \\ \\ x \\in \\Omega, \\ \\ u=0 \\quad \\text{on} \\ \\ \\partial \\Omega, \\] where $\\Omega \\subset {\\mathbb R}^2$ is either a ball or an annulus centered at the origin, $\\alpha >0$ and $f: {\\mathbb R}\\ \\rightarrow {\\mathbb R}$ is $C^{1, \\beta}$ on bounded sets of ${\\mathbb R}$. We address the question of estimating the Morse index $m(u)$ of a sign changing radial solution $u$. We prove that $m(u) \\geq 3$ for every $\\alpha>0$ and that $m(u)\\geq \\alpha+ 3$ if $\\alpha$ is even. 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