{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:VUBLVBAR4WM7Y2S74R6M7OQIOK","short_pith_number":"pith:VUBLVBAR","schema_version":"1.0","canonical_sha256":"ad02ba8411e599fc6a5fe47ccfba0872bd7cf18167dbd0667b631040c66b640e","source":{"kind":"arxiv","id":"1402.3516","version":2},"attestation_state":"computed","paper":{"title":"Hamiltonian elliptic systems: a guide to variational frameworks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Denis Bonheure, Ederson Moreira dos Santos, Hugo Tavares","submitted_at":"2014-02-14T16:15:43Z","abstract_excerpt":"Consider a Hamiltonian system of type \\[ -\\Delta u=H_{v}(u,v),\\ -\\Delta v=H_{u}(u,v) \\ \\ \\text{ in } \\Omega, \\qquad u,v=0 \\text{ on } \\partial \\Omega \\] where $H$ is a power-type nonlinearity, for instance $H(u,v)= |u|^p/p+|v|^q/q$, having subcritical growth, and $\\Omega$ is a bounded domain of $\\mathbb{R}^N$, $N\\geq 1$. The aim of this paper is to give an overview of the several variational frameworks that can be used to treat such a system. Within each approach, we address existence of solutions, and in particular of ground state solutions. Some of the available frameworks are more adequate "},"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":"1402.3516","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-14T16:15:43Z","cross_cats_sorted":[],"title_canon_sha256":"0d81a046f108e98e0d0c6f88fd491b5d391676a371709a58e4dfd9fab26eea77","abstract_canon_sha256":"71d1275a37bfe55cbf043b2434c9e889d18f95f8725027b94eeada0030a95eea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:41.343001Z","signature_b64":"OO3bo3+axrS1n0hw2DnJfqYpEPsDGx8iR8Ya5H9HriUaVuDP/G9qBh/P6ulhK05HvYC24QyShmL3Z1XKuwkXAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad02ba8411e599fc6a5fe47ccfba0872bd7cf18167dbd0667b631040c66b640e","last_reissued_at":"2026-05-18T02:16:41.342245Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:41.342245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hamiltonian elliptic systems: a guide to variational frameworks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Denis Bonheure, Ederson Moreira dos Santos, Hugo Tavares","submitted_at":"2014-02-14T16:15:43Z","abstract_excerpt":"Consider a Hamiltonian system of type \\[ -\\Delta u=H_{v}(u,v),\\ -\\Delta v=H_{u}(u,v) \\ \\ \\text{ in } \\Omega, \\qquad u,v=0 \\text{ on } \\partial \\Omega \\] where $H$ is a power-type nonlinearity, for instance $H(u,v)= |u|^p/p+|v|^q/q$, having subcritical growth, and $\\Omega$ is a bounded domain of $\\mathbb{R}^N$, $N\\geq 1$. The aim of this paper is to give an overview of the several variational frameworks that can be used to treat such a system. Within each approach, we address existence of solutions, and in particular of ground state solutions. Some of the available frameworks are more adequate "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3516","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":"1402.3516","created_at":"2026-05-18T02:16:41.342361+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.3516v2","created_at":"2026-05-18T02:16:41.342361+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3516","created_at":"2026-05-18T02:16:41.342361+00:00"},{"alias_kind":"pith_short_12","alias_value":"VUBLVBAR4WM7","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"VUBLVBAR4WM7Y2S7","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"VUBLVBAR","created_at":"2026-05-18T12:28:54.890064+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/VUBLVBAR4WM7Y2S74R6M7OQIOK","json":"https://pith.science/pith/VUBLVBAR4WM7Y2S74R6M7OQIOK.json","graph_json":"https://pith.science/api/pith-number/VUBLVBAR4WM7Y2S74R6M7OQIOK/graph.json","events_json":"https://pith.science/api/pith-number/VUBLVBAR4WM7Y2S74R6M7OQIOK/events.json","paper":"https://pith.science/paper/VUBLVBAR"},"agent_actions":{"view_html":"https://pith.science/pith/VUBLVBAR4WM7Y2S74R6M7OQIOK","download_json":"https://pith.science/pith/VUBLVBAR4WM7Y2S74R6M7OQIOK.json","view_paper":"https://pith.science/paper/VUBLVBAR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.3516&json=true","fetch_graph":"https://pith.science/api/pith-number/VUBLVBAR4WM7Y2S74R6M7OQIOK/graph.json","fetch_events":"https://pith.science/api/pith-number/VUBLVBAR4WM7Y2S74R6M7OQIOK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VUBLVBAR4WM7Y2S74R6M7OQIOK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VUBLVBAR4WM7Y2S74R6M7OQIOK/action/storage_attestation","attest_author":"https://pith.science/pith/VUBLVBAR4WM7Y2S74R6M7OQIOK/action/author_attestation","sign_citation":"https://pith.science/pith/VUBLVBAR4WM7Y2S74R6M7OQIOK/action/citation_signature","submit_replication":"https://pith.science/pith/VUBLVBAR4WM7Y2S74R6M7OQIOK/action/replication_record"}},"created_at":"2026-05-18T02:16:41.342361+00:00","updated_at":"2026-05-18T02:16:41.342361+00:00"}