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We will prove the existence of radially symmetric solution of the equation $\\Delta(f^m/m)+\\alpha f+\\beta x\\cdot\\nabla f=0$, $f>0$, in $\\mathbb{R}^n$, which satisfies $f(0)=\\eta_0$, $f_r(0)=0$. When $\\beta<\\frac{m\\rho_1}{n-2-nm}$ holds instead, we will also prove the existence of radially symmetric solution of the equation $\\Delta(f^m/m)+\\alpha f+\\beta x\\cdot\\nabla f=0$, $f>0$, in $\\mathbb{R}^n\\setminus\\{0\\}$, which satisfies $\\lim_{x\\to\\i"},"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":"2505.24131","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-05-30T01:58:25Z","cross_cats_sorted":[],"title_canon_sha256":"28f7a18be09433b1373d6202f094cb7d1b591898dbdb1740d7bd900527f97177","abstract_canon_sha256":"04685b1f0ad0bd625791672e7af35fe837fed9778db76fa092e9e22dc9ba143f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:12:42.548634Z","signature_b64":"pXdBDbUXIVe9vZXR1DlHe6qsMCwm16Q8VCwXrkdiaQlV+r1Yc2MhpU7FS0s/9gY0a2z3bNQ70d7XGwj87xZgCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60a866d338ea762280c3a979515c3442f36840a4889683bda082b2d8c7a74be1","last_reissued_at":"2026-07-05T11:12:42.544609Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:12:42.544609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of new self-similar solutions of the fast diffusion equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kin Ming Hui","submitted_at":"2025-05-30T01:58:25Z","abstract_excerpt":"Let $n\\ge 3$, $0<m<\\frac{n-2}{n}$, $\\eta>0$, $\\eta_0>0$, $\\rho_1>0$, $-\\frac{\\rho_1}{2}<\\beta<\\frac{m\\rho_1}{n-2-nm}$ and $\\alpha=\\frac{2\\beta+\\rho_1}{1-m}$. We will prove the existence of radially symmetric solution of the equation $\\Delta(f^m/m)+\\alpha f+\\beta x\\cdot\\nabla f=0$, $f>0$, in $\\mathbb{R}^n$, which satisfies $f(0)=\\eta_0$, $f_r(0)=0$. When $\\beta<\\frac{m\\rho_1}{n-2-nm}$ holds instead, we will also prove the existence of radially symmetric solution of the equation $\\Delta(f^m/m)+\\alpha f+\\beta x\\cdot\\nabla f=0$, $f>0$, in $\\mathbb{R}^n\\setminus\\{0\\}$, which satisfies $\\lim_{x\\to\\i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24131","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.24131/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2505.24131","created_at":"2026-07-05T11:12:42.547336+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.24131v1","created_at":"2026-07-05T11:12:42.547336+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.24131","created_at":"2026-07-05T11:12:42.547336+00:00"},{"alias_kind":"pith_short_12","alias_value":"MCUGNUZY5J3C","created_at":"2026-07-05T11:12:42.547336+00:00"},{"alias_kind":"pith_short_16","alias_value":"MCUGNUZY5J3CFAGD","created_at":"2026-07-05T11:12:42.547336+00:00"},{"alias_kind":"pith_short_8","alias_value":"MCUGNUZY","created_at":"2026-07-05T11:12:42.547336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MCUGNUZY5J3CFAGDVF4VCXBUIL","json":"https://pith.science/pith/MCUGNUZY5J3CFAGDVF4VCXBUIL.json","graph_json":"https://pith.science/api/pith-number/MCUGNUZY5J3CFAGDVF4VCXBUIL/graph.json","events_json":"https://pith.science/api/pith-number/MCUGNUZY5J3CFAGDVF4VCXBUIL/events.json","paper":"https://pith.science/paper/MCUGNUZY"},"agent_actions":{"view_html":"https://pith.science/pith/MCUGNUZY5J3CFAGDVF4VCXBUIL","download_json":"https://pith.science/pith/MCUGNUZY5J3CFAGDVF4VCXBUIL.json","view_paper":"https://pith.science/paper/MCUGNUZY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.24131&json=true","fetch_graph":"https://pith.science/api/pith-number/MCUGNUZY5J3CFAGDVF4VCXBUIL/graph.json","fetch_events":"https://pith.science/api/pith-number/MCUGNUZY5J3CFAGDVF4VCXBUIL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MCUGNUZY5J3CFAGDVF4VCXBUIL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MCUGNUZY5J3CFAGDVF4VCXBUIL/action/storage_attestation","attest_author":"https://pith.science/pith/MCUGNUZY5J3CFAGDVF4VCXBUIL/action/author_attestation","sign_citation":"https://pith.science/pith/MCUGNUZY5J3CFAGDVF4VCXBUIL/action/citation_signature","submit_replication":"https://pith.science/pith/MCUGNUZY5J3CFAGDVF4VCXBUIL/action/replication_record"}},"created_at":"2026-07-05T11:12:42.547336+00:00","updated_at":"2026-07-05T11:12:42.547336+00:00"}