{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:YYLN2V42SPZTT7AQQMTF4CR5NH","short_pith_number":"pith:YYLN2V42","schema_version":"1.0","canonical_sha256":"c616dd579a93f339fc1083265e0a3d69dd9534f502c91aae52cb917391a13f71","source":{"kind":"arxiv","id":"1211.5769","version":1},"attestation_state":"computed","paper":{"title":"Positive and sign changing solutions to a nonlinear Choquard equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dora Salazar, M\\'onica Clapp","submitted_at":"2012-11-25T15:51:06Z","abstract_excerpt":"We consider the problem \\[-\\Delta u + W(x)u = ((1/{|x|^{\\alpha}} * |u|^{p}) |u|^{p-2}u, u \\in H_{0}^{1}(\\Omega)\\], where $\\Omega$ is an exterior domain in $\\mathbb{R}^{N}$, $N\\geq3,$ $\\alpha \\in(0,N)$, $p\\in[2,(2N-\\alpha)/(N-2)$, $W$ is continuous, $\\inf_{\\mathbb{R}^{N}}W>0,$ and $W(x)$ tends to a positive constant as $|x|$ tends to infinity. Under symmetry assumptions on $\\Omega$ and $W$, which allow finite symmetries, and some assumptions on the decay of $W$ at infinity, we establish the existence of a positive solution and multiple sign changing solutions to this problem, having small energ"},"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":"1211.5769","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-25T15:51:06Z","cross_cats_sorted":[],"title_canon_sha256":"21d89ea2178b276667fa9d3685b88053a00be0481b84cce4624e113a4a22b9f1","abstract_canon_sha256":"f752950d2fc472c08808d8049c0bd765cfd57370465b1f4b8d2b951ccca4574c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:01.971526Z","signature_b64":"hkzmDyvU4VuimBhsh6bygE9UpjQY2KDRCPS0mV+OCGnidar9rxxD+ZFvUt/utYQjpZNK0hGGGOz9hfU/U2P0DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c616dd579a93f339fc1083265e0a3d69dd9534f502c91aae52cb917391a13f71","last_reissued_at":"2026-05-18T03:40:01.970877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:01.970877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Positive and sign changing solutions to a nonlinear Choquard equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dora Salazar, M\\'onica Clapp","submitted_at":"2012-11-25T15:51:06Z","abstract_excerpt":"We consider the problem \\[-\\Delta u + W(x)u = ((1/{|x|^{\\alpha}} * |u|^{p}) |u|^{p-2}u, u \\in H_{0}^{1}(\\Omega)\\], where $\\Omega$ is an exterior domain in $\\mathbb{R}^{N}$, $N\\geq3,$ $\\alpha \\in(0,N)$, $p\\in[2,(2N-\\alpha)/(N-2)$, $W$ is continuous, $\\inf_{\\mathbb{R}^{N}}W>0,$ and $W(x)$ tends to a positive constant as $|x|$ tends to infinity. Under symmetry assumptions on $\\Omega$ and $W$, which allow finite symmetries, and some assumptions on the decay of $W$ at infinity, we establish the existence of a positive solution and multiple sign changing solutions to this problem, having small energ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5769","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":"1211.5769","created_at":"2026-05-18T03:40:01.970964+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.5769v1","created_at":"2026-05-18T03:40:01.970964+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5769","created_at":"2026-05-18T03:40:01.970964+00:00"},{"alias_kind":"pith_short_12","alias_value":"YYLN2V42SPZT","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"YYLN2V42SPZTT7AQ","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"YYLN2V42","created_at":"2026-05-18T12:27:30.460161+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/YYLN2V42SPZTT7AQQMTF4CR5NH","json":"https://pith.science/pith/YYLN2V42SPZTT7AQQMTF4CR5NH.json","graph_json":"https://pith.science/api/pith-number/YYLN2V42SPZTT7AQQMTF4CR5NH/graph.json","events_json":"https://pith.science/api/pith-number/YYLN2V42SPZTT7AQQMTF4CR5NH/events.json","paper":"https://pith.science/paper/YYLN2V42"},"agent_actions":{"view_html":"https://pith.science/pith/YYLN2V42SPZTT7AQQMTF4CR5NH","download_json":"https://pith.science/pith/YYLN2V42SPZTT7AQQMTF4CR5NH.json","view_paper":"https://pith.science/paper/YYLN2V42","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.5769&json=true","fetch_graph":"https://pith.science/api/pith-number/YYLN2V42SPZTT7AQQMTF4CR5NH/graph.json","fetch_events":"https://pith.science/api/pith-number/YYLN2V42SPZTT7AQQMTF4CR5NH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YYLN2V42SPZTT7AQQMTF4CR5NH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YYLN2V42SPZTT7AQQMTF4CR5NH/action/storage_attestation","attest_author":"https://pith.science/pith/YYLN2V42SPZTT7AQQMTF4CR5NH/action/author_attestation","sign_citation":"https://pith.science/pith/YYLN2V42SPZTT7AQQMTF4CR5NH/action/citation_signature","submit_replication":"https://pith.science/pith/YYLN2V42SPZTT7AQQMTF4CR5NH/action/replication_record"}},"created_at":"2026-05-18T03:40:01.970964+00:00","updated_at":"2026-05-18T03:40:01.970964+00:00"}