{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:KPJROZG66MGR3DZKOZ5GTYC5CD","short_pith_number":"pith:KPJROZG6","schema_version":"1.0","canonical_sha256":"53d31764def30d1d8f2a767a69e05d10c876105e4a308140142a18575c49b8bf","source":{"kind":"arxiv","id":"1611.08756","version":1},"attestation_state":"computed","paper":{"title":"L$^p$-Solutions of a Nonlinear Third Order Differential Equation and Asymptotic Behavior of Linear Fourth Order Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DS","authors_text":"An\\'ibal Coronel, Fernando Huancas, Manuel Pinto","submitted_at":"2016-11-26T22:56:55Z","abstract_excerpt":"In this paper we prove the well-posedness and we study the asymptotic behavior of nonoscillatory $L^p$-solutions for a third order nonlinear scalar differential equation. The equation consists of two parts: a linear third order with constant coefficients part and a nonlinear part represented by a polynomial of fourth order in three variables with variable coefficients. The results are obtained assuming three hypotheses: (i) the characteristic polynomial associated with the linear part has simple and real roots, (ii) the coefficients of the polynomial satisfy asymptotic integral smallness condi"},"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":"1611.08756","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-11-26T22:56:55Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"2cca4365106596d05e85f6975de7aaba556abb6ce0ca21b1b2563159e95ba5ac","abstract_canon_sha256":"f38feaa8e84c1ede046c09bd26752434de15cf4d8d08158f53fb0fe3c18d5aeb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:54.184980Z","signature_b64":"x0tkhXYNN9hkzlem8ClOw3SMNCXUoXXu6uwriSX0/KmMzA8J30UHM7s2auUiWcCq2VP0l/K0ge3mgQTfAaEOBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53d31764def30d1d8f2a767a69e05d10c876105e4a308140142a18575c49b8bf","last_reissued_at":"2026-05-18T00:55:54.184584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:54.184584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"L$^p$-Solutions of a Nonlinear Third Order Differential Equation and Asymptotic Behavior of Linear Fourth Order Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DS","authors_text":"An\\'ibal Coronel, Fernando Huancas, Manuel Pinto","submitted_at":"2016-11-26T22:56:55Z","abstract_excerpt":"In this paper we prove the well-posedness and we study the asymptotic behavior of nonoscillatory $L^p$-solutions for a third order nonlinear scalar differential equation. The equation consists of two parts: a linear third order with constant coefficients part and a nonlinear part represented by a polynomial of fourth order in three variables with variable coefficients. The results are obtained assuming three hypotheses: (i) the characteristic polynomial associated with the linear part has simple and real roots, (ii) the coefficients of the polynomial satisfy asymptotic integral smallness condi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08756","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":"1611.08756","created_at":"2026-05-18T00:55:54.184654+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.08756v1","created_at":"2026-05-18T00:55:54.184654+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08756","created_at":"2026-05-18T00:55:54.184654+00:00"},{"alias_kind":"pith_short_12","alias_value":"KPJROZG66MGR","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"KPJROZG66MGR3DZK","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"KPJROZG6","created_at":"2026-05-18T12:30:25.849896+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/KPJROZG66MGR3DZKOZ5GTYC5CD","json":"https://pith.science/pith/KPJROZG66MGR3DZKOZ5GTYC5CD.json","graph_json":"https://pith.science/api/pith-number/KPJROZG66MGR3DZKOZ5GTYC5CD/graph.json","events_json":"https://pith.science/api/pith-number/KPJROZG66MGR3DZKOZ5GTYC5CD/events.json","paper":"https://pith.science/paper/KPJROZG6"},"agent_actions":{"view_html":"https://pith.science/pith/KPJROZG66MGR3DZKOZ5GTYC5CD","download_json":"https://pith.science/pith/KPJROZG66MGR3DZKOZ5GTYC5CD.json","view_paper":"https://pith.science/paper/KPJROZG6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.08756&json=true","fetch_graph":"https://pith.science/api/pith-number/KPJROZG66MGR3DZKOZ5GTYC5CD/graph.json","fetch_events":"https://pith.science/api/pith-number/KPJROZG66MGR3DZKOZ5GTYC5CD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KPJROZG66MGR3DZKOZ5GTYC5CD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KPJROZG66MGR3DZKOZ5GTYC5CD/action/storage_attestation","attest_author":"https://pith.science/pith/KPJROZG66MGR3DZKOZ5GTYC5CD/action/author_attestation","sign_citation":"https://pith.science/pith/KPJROZG66MGR3DZKOZ5GTYC5CD/action/citation_signature","submit_replication":"https://pith.science/pith/KPJROZG66MGR3DZKOZ5GTYC5CD/action/replication_record"}},"created_at":"2026-05-18T00:55:54.184654+00:00","updated_at":"2026-05-18T00:55:54.184654+00:00"}