{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ZPFOP767RPPU3VU3VXYJ74RBSD","short_pith_number":"pith:ZPFOP767","schema_version":"1.0","canonical_sha256":"cbcae7ffdf8bdf4dd69badf09ff22190e12ac4df8d6584e9b114f0c44f700c26","source":{"kind":"arxiv","id":"1612.01071","version":1},"attestation_state":"computed","paper":{"title":"Liouville theorem for the fractional Lane-Emden Equation in unbounded domain","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huyuan Chen","submitted_at":"2016-12-04T05:35:40Z","abstract_excerpt":"Our purpose of this paper is to study the nonexistence of nonnegative very weak solutions of \\begin{equation}\\label{eq 0.1}\n  \\displaystyle (-\\Delta)^\\alpha u = u^p+\\nu\\quad\n  {\\rm in}\\quad \\Omega,\\qquad\\ u=g\\quad {\\rm in}\\quad \\mathbb{ R}^N\\setminus \\Omega,\n  \\end{equation} where $\\alpha\\in(0,1)$, $p>0$, $\\Omega$ is a unbounded $C^2$ domain in $\\mathbb{ R}^N$ with $N>2\\alpha$, $g\\in L^1(\\mathbb{ R}^N\\setminus \\Omega,\\frac{dx}{1+|x|^{N+2\\alpha}})$ nonnegative and $\\nu$ is a nonnegative Radon measure. We obtain that\\smallskip\n  $(i)$ if $\\Omega\\supseteq \\left(\\mathbb{R}^N\\setminus \\overline{B_{"},"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":"1612.01071","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2016-12-04T05:35:40Z","cross_cats_sorted":[],"title_canon_sha256":"73d80680e375773091ef4d4ee1433d1f5c7b08c4e73fcffb5d4e9d7e34b7ac8b","abstract_canon_sha256":"86a25d8bdb9ba64a3eb074740c614cd3740bcb5ecd142acc5d4833a2f059c71b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:53.427251Z","signature_b64":"zctk0jUekS/aBrRGlCM/idnYjrlHPy1MvZCXUW49MG3FDVn3lLWfkgVlPD2qHU6i8x01OpF4m4g1P3pRJjxoDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbcae7ffdf8bdf4dd69badf09ff22190e12ac4df8d6584e9b114f0c44f700c26","last_reissued_at":"2026-05-18T00:55:53.426853Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:53.426853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Liouville theorem for the fractional Lane-Emden Equation in unbounded domain","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huyuan Chen","submitted_at":"2016-12-04T05:35:40Z","abstract_excerpt":"Our purpose of this paper is to study the nonexistence of nonnegative very weak solutions of \\begin{equation}\\label{eq 0.1}\n  \\displaystyle (-\\Delta)^\\alpha u = u^p+\\nu\\quad\n  {\\rm in}\\quad \\Omega,\\qquad\\ u=g\\quad {\\rm in}\\quad \\mathbb{ R}^N\\setminus \\Omega,\n  \\end{equation} where $\\alpha\\in(0,1)$, $p>0$, $\\Omega$ is a unbounded $C^2$ domain in $\\mathbb{ R}^N$ with $N>2\\alpha$, $g\\in L^1(\\mathbb{ R}^N\\setminus \\Omega,\\frac{dx}{1+|x|^{N+2\\alpha}})$ nonnegative and $\\nu$ is a nonnegative Radon measure. We obtain that\\smallskip\n  $(i)$ if $\\Omega\\supseteq \\left(\\mathbb{R}^N\\setminus \\overline{B_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01071","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":""},"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":"1612.01071","created_at":"2026-05-18T00:55:53.426913+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.01071v1","created_at":"2026-05-18T00:55:53.426913+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01071","created_at":"2026-05-18T00:55:53.426913+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZPFOP767RPPU","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZPFOP767RPPU3VU3","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZPFOP767","created_at":"2026-05-18T12:30:55.937587+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/ZPFOP767RPPU3VU3VXYJ74RBSD","json":"https://pith.science/pith/ZPFOP767RPPU3VU3VXYJ74RBSD.json","graph_json":"https://pith.science/api/pith-number/ZPFOP767RPPU3VU3VXYJ74RBSD/graph.json","events_json":"https://pith.science/api/pith-number/ZPFOP767RPPU3VU3VXYJ74RBSD/events.json","paper":"https://pith.science/paper/ZPFOP767"},"agent_actions":{"view_html":"https://pith.science/pith/ZPFOP767RPPU3VU3VXYJ74RBSD","download_json":"https://pith.science/pith/ZPFOP767RPPU3VU3VXYJ74RBSD.json","view_paper":"https://pith.science/paper/ZPFOP767","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.01071&json=true","fetch_graph":"https://pith.science/api/pith-number/ZPFOP767RPPU3VU3VXYJ74RBSD/graph.json","fetch_events":"https://pith.science/api/pith-number/ZPFOP767RPPU3VU3VXYJ74RBSD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZPFOP767RPPU3VU3VXYJ74RBSD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZPFOP767RPPU3VU3VXYJ74RBSD/action/storage_attestation","attest_author":"https://pith.science/pith/ZPFOP767RPPU3VU3VXYJ74RBSD/action/author_attestation","sign_citation":"https://pith.science/pith/ZPFOP767RPPU3VU3VXYJ74RBSD/action/citation_signature","submit_replication":"https://pith.science/pith/ZPFOP767RPPU3VU3VXYJ74RBSD/action/replication_record"}},"created_at":"2026-05-18T00:55:53.426913+00:00","updated_at":"2026-05-18T00:55:53.426913+00:00"}