{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:CSCHNXVAJX5ML27VGQJNP25QN2","short_pith_number":"pith:CSCHNXVA","schema_version":"1.0","canonical_sha256":"148476dea04dfac5ebf53412d7ebb06eb0f43ce6e5694191a0014d522a90bb79","source":{"kind":"arxiv","id":"1312.5871","version":1},"attestation_state":"computed","paper":{"title":"Asymptotic analysis for radial sign-changing solutions of the Brezis-Nirenberg problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Iacopetti","submitted_at":"2013-12-20T10:18:54Z","abstract_excerpt":"We study the asymptotic behavior, as $\\lambda \\rightarrow 0$, of least energy radial sign-changing solutions $u_\\lambda$, of the Brezis-Nirenberg problem\n  \\begin{equation*} \\begin{cases} -\\Delta u = \\lambda u + |u|^{2^* -2}u & \\hbox{in}\\ B_1\\\\ u=0 & \\hbox{on}\\ \\partial B_1, \\end{cases} \\end{equation*} where $\\lambda >0$, $2^*=\\frac{2n}{n-2}$ and $B_1$ is the unit ball of $\\R^n$, $n\\geq 7$.\n  We prove that both the positive and negative part $u_\\lambda^+$ and $u_\\lambda^-$ concentrate at the same point (which is the center) of the ball with different concentration speeds. Moreover we show that"},"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":"1312.5871","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-20T10:18:54Z","cross_cats_sorted":[],"title_canon_sha256":"fea7cf07641e2bf80b59e9248b64a4c59593d3a78234a41a4fb976778f6a7f08","abstract_canon_sha256":"b3e2a9bff36382b3f8b8e876b0b9804b4e13452780bdb76f82111cefa7242d6c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:07.645356Z","signature_b64":"V3g57IYCJ/2zoqfpxbKlMErqfoN7fpmsjzuTHOi87OYMhdLYbC0DhT6p2BsprQ5tyjfVWkw9ZhEcQKTcsZ9KDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"148476dea04dfac5ebf53412d7ebb06eb0f43ce6e5694191a0014d522a90bb79","last_reissued_at":"2026-05-18T03:04:07.644790Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:07.644790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic analysis for radial sign-changing solutions of the Brezis-Nirenberg problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Iacopetti","submitted_at":"2013-12-20T10:18:54Z","abstract_excerpt":"We study the asymptotic behavior, as $\\lambda \\rightarrow 0$, of least energy radial sign-changing solutions $u_\\lambda$, of the Brezis-Nirenberg problem\n  \\begin{equation*} \\begin{cases} -\\Delta u = \\lambda u + |u|^{2^* -2}u & \\hbox{in}\\ B_1\\\\ u=0 & \\hbox{on}\\ \\partial B_1, \\end{cases} \\end{equation*} where $\\lambda >0$, $2^*=\\frac{2n}{n-2}$ and $B_1$ is the unit ball of $\\R^n$, $n\\geq 7$.\n  We prove that both the positive and negative part $u_\\lambda^+$ and $u_\\lambda^-$ concentrate at the same point (which is the center) of the ball with different concentration speeds. 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