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Neves","submitted_at":"2017-08-30T04:34:29Z","abstract_excerpt":"We consider the H\\'enon problem \\begin{equation*} \\left\\{ \\begin{array} - - \\Delta u = |x|^{\\alpha} u^{\\frac{N+2+2\\alpha}{N-2}-\\varepsilon} & \\ \\ \\text{in} \\ B_1, \\\\ u > 0 & \\ \\ \\text{in} \\ B_1, \\\\ u=0 & \\ \\ \\text{on} \\ \\partial B_1, \\end{array} \\right. \\end{equation*} where $B_1$ is the unit ball in ${\\mathbb R}^N$ and $N\\geqslant 3$. For $\\varepsilon > 0$ small enough, we use $\\alpha$ as a paramenter and prove the existence of a branch of nonradial solutions that bifurcates from the radial one when $\\alpha$ is close to an even positive integer."},"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":"1708.09112","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-30T04:34:29Z","cross_cats_sorted":[],"title_canon_sha256":"4729351ed77e4677576332e27e6d55186270adbd145c1c7c93198061943cd3eb","abstract_canon_sha256":"6c80ea390714f8398cd3eebe3a42811faf8f6bf20643b7e0c92962493f3fdcf4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:58.549592Z","signature_b64":"LPQIJhB64jYXsKcvK1E5sdgJF5jF6bV/ymw6v4eC4O75Qt5RjIYAcu/EP4zaXtmHNW2Hw8rsRi8oazf10XgrBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a4986b919e7a5616192beadffcba73fb60460d0e5c67a384b76bb0a664751c8","last_reissued_at":"2026-05-18T00:33:58.548998Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:58.548998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonradial solutions for the H\\'enon equation close to the threshold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pablo Figueroa, S\\'ergio L. 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