{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:OHJROVOLU5DNXFRHN4OK44V7FK","short_pith_number":"pith:OHJROVOL","schema_version":"1.0","canonical_sha256":"71d31755cba746db96276f1cae72bf2aafcbac0edc7bd33b20e81697a886cd98","source":{"kind":"arxiv","id":"2107.04995","version":1},"attestation_state":"computed","paper":{"title":"Liouville theorem on a half-space for biharmonic problem with Dirichlet boundary condition","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Abdelbaki Selmi, Cherif Zaid, Foued Mtiri","submitted_at":"2021-07-11T08:55:15Z","abstract_excerpt":"We investigate here the nonlinear elliptic H\\'enon type equation:\n  $$\\D^{2} u= |x|^a|u|^{p-1}u \\; \\,\\,\\mbox{in}\\,\\,\\,\\, \\R^{n}_{+}, \\quad \\quad u =\\frac{\\partial u}{\\partial x_n} = 0 \\quad \\mbox{in}\\,\\,\\,\\, \\partial \\R^{n}_{+},$$ with $p>1$ and $n\\geq 2$. In particular, we prove some Liouville type theorems for stable at infinity solutions. The main methods used are the integral estimates, the Pohozaev-type identity and the monotonicity formula."},"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":"2107.04995","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-07-11T08:55:15Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"c0e496120958d61c0b4b43f6932e748acf1225b49ff1b22fb413b42a703eaa41","abstract_canon_sha256":"5b02efb58cc6da0e19bbfd8b629ccad0888ec65a5d1d1f971006b6ff9fe1c1bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:56:45.157702Z","signature_b64":"ukUTYQvNCph9QjjWeathCaPl68gd557s2p4OE7zKQK/KAiv8DxjImRlvA2QcThHM87HeSbK7oGl8Di1HE5ICBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71d31755cba746db96276f1cae72bf2aafcbac0edc7bd33b20e81697a886cd98","last_reissued_at":"2026-07-05T02:56:45.157200Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:56:45.157200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Liouville theorem on a half-space for biharmonic problem with Dirichlet boundary condition","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Abdelbaki Selmi, Cherif Zaid, Foued Mtiri","submitted_at":"2021-07-11T08:55:15Z","abstract_excerpt":"We investigate here the nonlinear elliptic H\\'enon type equation:\n  $$\\D^{2} u= |x|^a|u|^{p-1}u \\; \\,\\,\\mbox{in}\\,\\,\\,\\, \\R^{n}_{+}, \\quad \\quad u =\\frac{\\partial u}{\\partial x_n} = 0 \\quad \\mbox{in}\\,\\,\\,\\, \\partial \\R^{n}_{+},$$ with $p>1$ and $n\\geq 2$. In particular, we prove some Liouville type theorems for stable at infinity solutions. The main methods used are the integral estimates, the Pohozaev-type identity and the monotonicity formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.04995","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/2107.04995/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":"2107.04995","created_at":"2026-07-05T02:56:45.157261+00:00"},{"alias_kind":"arxiv_version","alias_value":"2107.04995v1","created_at":"2026-07-05T02:56:45.157261+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.04995","created_at":"2026-07-05T02:56:45.157261+00:00"},{"alias_kind":"pith_short_12","alias_value":"OHJROVOLU5DN","created_at":"2026-07-05T02:56:45.157261+00:00"},{"alias_kind":"pith_short_16","alias_value":"OHJROVOLU5DNXFRH","created_at":"2026-07-05T02:56:45.157261+00:00"},{"alias_kind":"pith_short_8","alias_value":"OHJROVOL","created_at":"2026-07-05T02:56:45.157261+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/OHJROVOLU5DNXFRHN4OK44V7FK","json":"https://pith.science/pith/OHJROVOLU5DNXFRHN4OK44V7FK.json","graph_json":"https://pith.science/api/pith-number/OHJROVOLU5DNXFRHN4OK44V7FK/graph.json","events_json":"https://pith.science/api/pith-number/OHJROVOLU5DNXFRHN4OK44V7FK/events.json","paper":"https://pith.science/paper/OHJROVOL"},"agent_actions":{"view_html":"https://pith.science/pith/OHJROVOLU5DNXFRHN4OK44V7FK","download_json":"https://pith.science/pith/OHJROVOLU5DNXFRHN4OK44V7FK.json","view_paper":"https://pith.science/paper/OHJROVOL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2107.04995&json=true","fetch_graph":"https://pith.science/api/pith-number/OHJROVOLU5DNXFRHN4OK44V7FK/graph.json","fetch_events":"https://pith.science/api/pith-number/OHJROVOLU5DNXFRHN4OK44V7FK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OHJROVOLU5DNXFRHN4OK44V7FK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OHJROVOLU5DNXFRHN4OK44V7FK/action/storage_attestation","attest_author":"https://pith.science/pith/OHJROVOLU5DNXFRHN4OK44V7FK/action/author_attestation","sign_citation":"https://pith.science/pith/OHJROVOLU5DNXFRHN4OK44V7FK/action/citation_signature","submit_replication":"https://pith.science/pith/OHJROVOLU5DNXFRHN4OK44V7FK/action/replication_record"}},"created_at":"2026-07-05T02:56:45.157261+00:00","updated_at":"2026-07-05T02:56:45.157261+00:00"}