{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6HPBD7SXUDYXKFSNEXT4ZJYQTY","short_pith_number":"pith:6HPBD7SX","schema_version":"1.0","canonical_sha256":"f1de11fe57a0f175164d25e7cca7109e29227ff738828842ce7c73412f57c953","source":{"kind":"arxiv","id":"1709.04822","version":2},"attestation_state":"computed","paper":{"title":"A curve of positive solutions for an indefinite sublinear Dirichlet problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Humberto Ramos Quoirin, Kenichiro Umezu, Uriel Kaufmann","submitted_at":"2017-09-14T14:50:39Z","abstract_excerpt":"We investigate the existence of a curve $q\\mapsto u_{q}$, with $q\\in(0,1)$, of positive solutions for the problem $(P_{a,q})$: $-\\Delta u=a(x)u^{q}$ in $\\Omega$, $u=0$ on $\\partial\\Omega$, where $\\Omega$ is a bounded and smooth domain of $\\mathbb{R}^{N}$ and $a:\\Omega\\rightarrow\\mathbb{R}$ is a sign-changing function (in which case the strong maximum principle does not hold). In addition, we analyze the asymptotic behavior of $u_{q}$ as $q\\rightarrow0^{+}$ and $q\\rightarrow1^{-}$. We also show that in some cases $u_{q}$ is the ground state solution of $(P_{a,q})$. As a byproduct, we obtain exi"},"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":"1709.04822","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-14T14:50:39Z","cross_cats_sorted":[],"title_canon_sha256":"7eb6682b352911820cc1a5b9c3f0547dbfe7d9c7b2bcde7b8738842c28ccd771","abstract_canon_sha256":"5e8391edbaf44187020215c5f50a0473d924bb38cfd083fb0caad29f9f1cdcac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:04.761526Z","signature_b64":"s6Z5gtCoKw3lyjAHvMRLqEyvnzwPhoAyHpRiVnhTDgK6JU57bhk0xNs6uplYw0NLWWlpXNTDFdVPUVkJwVRtAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1de11fe57a0f175164d25e7cca7109e29227ff738828842ce7c73412f57c953","last_reissued_at":"2026-05-17T23:40:04.760856Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:04.760856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A curve of positive solutions for an indefinite sublinear Dirichlet problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Humberto Ramos Quoirin, Kenichiro Umezu, Uriel Kaufmann","submitted_at":"2017-09-14T14:50:39Z","abstract_excerpt":"We investigate the existence of a curve $q\\mapsto u_{q}$, with $q\\in(0,1)$, of positive solutions for the problem $(P_{a,q})$: $-\\Delta u=a(x)u^{q}$ in $\\Omega$, $u=0$ on $\\partial\\Omega$, where $\\Omega$ is a bounded and smooth domain of $\\mathbb{R}^{N}$ and $a:\\Omega\\rightarrow\\mathbb{R}$ is a sign-changing function (in which case the strong maximum principle does not hold). In addition, we analyze the asymptotic behavior of $u_{q}$ as $q\\rightarrow0^{+}$ and $q\\rightarrow1^{-}$. We also show that in some cases $u_{q}$ is the ground state solution of $(P_{a,q})$. As a byproduct, we obtain exi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04822","kind":"arxiv","version":2},"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":"1709.04822","created_at":"2026-05-17T23:40:04.760940+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.04822v2","created_at":"2026-05-17T23:40:04.760940+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04822","created_at":"2026-05-17T23:40:04.760940+00:00"},{"alias_kind":"pith_short_12","alias_value":"6HPBD7SXUDYX","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6HPBD7SXUDYXKFSN","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6HPBD7SX","created_at":"2026-05-18T12:31:03.183658+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/6HPBD7SXUDYXKFSNEXT4ZJYQTY","json":"https://pith.science/pith/6HPBD7SXUDYXKFSNEXT4ZJYQTY.json","graph_json":"https://pith.science/api/pith-number/6HPBD7SXUDYXKFSNEXT4ZJYQTY/graph.json","events_json":"https://pith.science/api/pith-number/6HPBD7SXUDYXKFSNEXT4ZJYQTY/events.json","paper":"https://pith.science/paper/6HPBD7SX"},"agent_actions":{"view_html":"https://pith.science/pith/6HPBD7SXUDYXKFSNEXT4ZJYQTY","download_json":"https://pith.science/pith/6HPBD7SXUDYXKFSNEXT4ZJYQTY.json","view_paper":"https://pith.science/paper/6HPBD7SX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.04822&json=true","fetch_graph":"https://pith.science/api/pith-number/6HPBD7SXUDYXKFSNEXT4ZJYQTY/graph.json","fetch_events":"https://pith.science/api/pith-number/6HPBD7SXUDYXKFSNEXT4ZJYQTY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6HPBD7SXUDYXKFSNEXT4ZJYQTY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6HPBD7SXUDYXKFSNEXT4ZJYQTY/action/storage_attestation","attest_author":"https://pith.science/pith/6HPBD7SXUDYXKFSNEXT4ZJYQTY/action/author_attestation","sign_citation":"https://pith.science/pith/6HPBD7SXUDYXKFSNEXT4ZJYQTY/action/citation_signature","submit_replication":"https://pith.science/pith/6HPBD7SXUDYXKFSNEXT4ZJYQTY/action/replication_record"}},"created_at":"2026-05-17T23:40:04.760940+00:00","updated_at":"2026-05-17T23:40:04.760940+00:00"}