{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:FN7ALGE2PHWIF77OG23ID7PDSG","short_pith_number":"pith:FN7ALGE2","schema_version":"1.0","canonical_sha256":"2b7e05989a79ec82ffee36b681fde391873f29fd8b038598333961facb3c51a4","source":{"kind":"arxiv","id":"1904.00841","version":1},"attestation_state":"computed","paper":{"title":"Positive solutions for semilinear fractional elliptic problems involving an inverse fractional operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alejandro Ortega, Eduardo Colorado, Pablo \\'Alvarez-Caudevilla","submitted_at":"2019-04-01T13:26:16Z","abstract_excerpt":"This paper is devoted to the study of the existence of positive solutions for a problem related to a higher order fractional differential equation involving a nonlinear term depending on a fractional differential operator, $$(-\\Delta)^{\\alpha} u=\\lambda u+ (-\\Delta)^{\\beta}|u|^{p-1}u \\quad \\mbox{in}\\quad \\Omega;\\qquad (-\\Delta)^{j}u=0\\quad \\mbox{on}\\quad \\partial\\Omega,\\quad \\mbox{for}\\quad j\\in\\mathbb{Z},\\: 0\\leq j< [\\alpha]$$ where $\\Omega$ is a bounded domain in $\\mathbb{R}^{N}$, $0<\\beta<1$, $\\beta<\\alpha<\\beta+1$ and $\\lambda>0$. In particular, we study the fractional elliptic problem, $$"},"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":"1904.00841","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-01T13:26:16Z","cross_cats_sorted":[],"title_canon_sha256":"a37fff06d9cf06b0e70a62eb1e6f12d8f7450288a59d0bbff85dce3cd8d5f5e2","abstract_canon_sha256":"a1b51fe9e6a985968b40d39b01ba3d9458e52544bcaa69196cfb619c72398309"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:45.347123Z","signature_b64":"Fc/jAcSkaBnQoZzZ7xJJoNM6yiTpL1h3feAbFKMGUjoBLhtB4GHGEjby6eODM5+ODH3y1ieaAQLH58SQt0gcBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b7e05989a79ec82ffee36b681fde391873f29fd8b038598333961facb3c51a4","last_reissued_at":"2026-05-17T23:49:45.346702Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:45.346702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Positive solutions for semilinear fractional elliptic problems involving an inverse fractional operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alejandro Ortega, Eduardo Colorado, Pablo \\'Alvarez-Caudevilla","submitted_at":"2019-04-01T13:26:16Z","abstract_excerpt":"This paper is devoted to the study of the existence of positive solutions for a problem related to a higher order fractional differential equation involving a nonlinear term depending on a fractional differential operator, $$(-\\Delta)^{\\alpha} u=\\lambda u+ (-\\Delta)^{\\beta}|u|^{p-1}u \\quad \\mbox{in}\\quad \\Omega;\\qquad (-\\Delta)^{j}u=0\\quad \\mbox{on}\\quad \\partial\\Omega,\\quad \\mbox{for}\\quad j\\in\\mathbb{Z},\\: 0\\leq j< [\\alpha]$$ where $\\Omega$ is a bounded domain in $\\mathbb{R}^{N}$, $0<\\beta<1$, $\\beta<\\alpha<\\beta+1$ and $\\lambda>0$. In particular, we study the fractional elliptic problem, $$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00841","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":"1904.00841","created_at":"2026-05-17T23:49:45.346761+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.00841v1","created_at":"2026-05-17T23:49:45.346761+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00841","created_at":"2026-05-17T23:49:45.346761+00:00"},{"alias_kind":"pith_short_12","alias_value":"FN7ALGE2PHWI","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"FN7ALGE2PHWIF77O","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"FN7ALGE2","created_at":"2026-05-18T12:33:15.570797+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/FN7ALGE2PHWIF77OG23ID7PDSG","json":"https://pith.science/pith/FN7ALGE2PHWIF77OG23ID7PDSG.json","graph_json":"https://pith.science/api/pith-number/FN7ALGE2PHWIF77OG23ID7PDSG/graph.json","events_json":"https://pith.science/api/pith-number/FN7ALGE2PHWIF77OG23ID7PDSG/events.json","paper":"https://pith.science/paper/FN7ALGE2"},"agent_actions":{"view_html":"https://pith.science/pith/FN7ALGE2PHWIF77OG23ID7PDSG","download_json":"https://pith.science/pith/FN7ALGE2PHWIF77OG23ID7PDSG.json","view_paper":"https://pith.science/paper/FN7ALGE2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.00841&json=true","fetch_graph":"https://pith.science/api/pith-number/FN7ALGE2PHWIF77OG23ID7PDSG/graph.json","fetch_events":"https://pith.science/api/pith-number/FN7ALGE2PHWIF77OG23ID7PDSG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FN7ALGE2PHWIF77OG23ID7PDSG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FN7ALGE2PHWIF77OG23ID7PDSG/action/storage_attestation","attest_author":"https://pith.science/pith/FN7ALGE2PHWIF77OG23ID7PDSG/action/author_attestation","sign_citation":"https://pith.science/pith/FN7ALGE2PHWIF77OG23ID7PDSG/action/citation_signature","submit_replication":"https://pith.science/pith/FN7ALGE2PHWIF77OG23ID7PDSG/action/replication_record"}},"created_at":"2026-05-17T23:49:45.346761+00:00","updated_at":"2026-05-17T23:49:45.346761+00:00"}