{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:CQ46P3SVFUVBTCPB3SRRMRDXZN","short_pith_number":"pith:CQ46P3SV","schema_version":"1.0","canonical_sha256":"1439e7ee552d2a1989e1dca3164477cb523ea6bbf527c3adc38361e20828c914","source":{"kind":"arxiv","id":"0904.4611","version":1},"attestation_state":"computed","paper":{"title":"Bound states for a stationary nonlinear Schrodinger-Poisson system with sign-changing potential in $R^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huan-Song Zhou, Yongsheng Jiang","submitted_at":"2009-04-29T13:49:03Z","abstract_excerpt":"We study the following Schr\\\"odinger-Poisson system (P_\\lambda){ll}\n  -\\Delta u + V(x)u+\\lambda \\phi (x) u =Q(x)u^{p}, x\\in \\mathbb{R}^3 \\\\\n  -\\Delta\\phi = u^2, \\lim\\limits_{|x|\\to +\\infty}\\phi(x)=0, u>0, where $\\lambda\\geqslant0$ is a parameter, $1 < p < +\\infty$, $V(x)$ and $Q(x)$ are sign-changing or non-positive functions in $ L^{\\infty}(\\mathbb{R}^3)$. When $V(x)\\equiv Q(x)\\equiv1$, D.Ruiz \\cite{RuizD-JFA} proved that ($P_\\lambda$) with $p\\in(2,5)$ has always a positive radial solution, but ($P_\\lambda$) with $p\\in(1,2]$ has solution only if $\\lambda>0$ small enough and no any nontrivial "},"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":"0904.4611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-04-29T13:49:03Z","cross_cats_sorted":[],"title_canon_sha256":"d8f14ded83fe35a5e0fddfdac648838ab35ef52dcdef1229e37fac22871aaca6","abstract_canon_sha256":"5cc0ced8ebef3ec156731db0b32b326301d74eee55fbae02a54b9d0a588f11bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:49.943069Z","signature_b64":"wmr4Dx1x7eT4/Zmdw3ZpXzpGUWHLQrQ5WA4cX5Jbsuq7GChMCo547Vi0IMzovAnCXXwbDH5vUsCCfZ0hb85HAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1439e7ee552d2a1989e1dca3164477cb523ea6bbf527c3adc38361e20828c914","last_reissued_at":"2026-05-18T02:27:49.942635Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:49.942635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bound states for a stationary nonlinear Schrodinger-Poisson system with sign-changing potential in $R^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huan-Song Zhou, Yongsheng Jiang","submitted_at":"2009-04-29T13:49:03Z","abstract_excerpt":"We study the following Schr\\\"odinger-Poisson system (P_\\lambda){ll}\n  -\\Delta u + V(x)u+\\lambda \\phi (x) u =Q(x)u^{p}, x\\in \\mathbb{R}^3 \\\\\n  -\\Delta\\phi = u^2, \\lim\\limits_{|x|\\to +\\infty}\\phi(x)=0, u>0, where $\\lambda\\geqslant0$ is a parameter, $1 < p < +\\infty$, $V(x)$ and $Q(x)$ are sign-changing or non-positive functions in $ L^{\\infty}(\\mathbb{R}^3)$. When $V(x)\\equiv Q(x)\\equiv1$, D.Ruiz \\cite{RuizD-JFA} proved that ($P_\\lambda$) with $p\\in(2,5)$ has always a positive radial solution, but ($P_\\lambda$) with $p\\in(1,2]$ has solution only if $\\lambda>0$ small enough and no any nontrivial "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4611","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":"0904.4611","created_at":"2026-05-18T02:27:49.942695+00:00"},{"alias_kind":"arxiv_version","alias_value":"0904.4611v1","created_at":"2026-05-18T02:27:49.942695+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.4611","created_at":"2026-05-18T02:27:49.942695+00:00"},{"alias_kind":"pith_short_12","alias_value":"CQ46P3SVFUVB","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_16","alias_value":"CQ46P3SVFUVBTCPB","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_8","alias_value":"CQ46P3SV","created_at":"2026-05-18T12:25:59.703012+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/CQ46P3SVFUVBTCPB3SRRMRDXZN","json":"https://pith.science/pith/CQ46P3SVFUVBTCPB3SRRMRDXZN.json","graph_json":"https://pith.science/api/pith-number/CQ46P3SVFUVBTCPB3SRRMRDXZN/graph.json","events_json":"https://pith.science/api/pith-number/CQ46P3SVFUVBTCPB3SRRMRDXZN/events.json","paper":"https://pith.science/paper/CQ46P3SV"},"agent_actions":{"view_html":"https://pith.science/pith/CQ46P3SVFUVBTCPB3SRRMRDXZN","download_json":"https://pith.science/pith/CQ46P3SVFUVBTCPB3SRRMRDXZN.json","view_paper":"https://pith.science/paper/CQ46P3SV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0904.4611&json=true","fetch_graph":"https://pith.science/api/pith-number/CQ46P3SVFUVBTCPB3SRRMRDXZN/graph.json","fetch_events":"https://pith.science/api/pith-number/CQ46P3SVFUVBTCPB3SRRMRDXZN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CQ46P3SVFUVBTCPB3SRRMRDXZN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CQ46P3SVFUVBTCPB3SRRMRDXZN/action/storage_attestation","attest_author":"https://pith.science/pith/CQ46P3SVFUVBTCPB3SRRMRDXZN/action/author_attestation","sign_citation":"https://pith.science/pith/CQ46P3SVFUVBTCPB3SRRMRDXZN/action/citation_signature","submit_replication":"https://pith.science/pith/CQ46P3SVFUVBTCPB3SRRMRDXZN/action/replication_record"}},"created_at":"2026-05-18T02:27:49.942695+00:00","updated_at":"2026-05-18T02:27:49.942695+00:00"}