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We investigate the existence and the nonexistence of positive classical solutions with the help of an integral system involving the Newton potential $$ \\left \\{ \\begin{array}{l} u(x)=c_1\\displaystyle\\int_{R^n}\\frac{u^{p-1}(y)v(y)dy}{|x-y|^{n-2}}, \\quad u>0 \\quad in \\quad R^n, v(x)=c_2\\displaystyle\\int_{R^n}\\frac{u^p(y)dy}{|x-y|^{n-2}} \\quad v>0 \\quad i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1411.1523","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-06T08:22:09Z","cross_cats_sorted":[],"title_canon_sha256":"c905b494f29159153b60a21207f6105d6d89ade099d59dfabda379cfd63f5e56","abstract_canon_sha256":"d66fdf94519d7fd721df1460477534df240c57d48b1607713174db0db799dd11"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:27.702262Z","signature_b64":"wrmmeB9fpgogaCriFVfVHhS+lgIp6xIXg63ZcQ0Jr8lUHqe53q96/RX/Jy8Ej5o2guY7lCdMO09bPASlmpWQAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f74dbb5ff8b0a88fb6fc3def648433fc130e6dc7286477e3ec31f539b0b8858","last_reissued_at":"2026-05-18T02:38:27.701757Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:27.701757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some existence and nonexistence results for a Schr\\\"odinger-Poisson type system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yutian Lei","submitted_at":"2014-11-06T08:22:09Z","abstract_excerpt":"In this paper, we study the Schr\\\"odinger-Poisson system $$ \\left \\{ \\begin{array}{l} -\\Delta u=\\sqrt{p}u^{p-1}v, \\quad u>0 \\quad in \\quad R^n, -\\Delta v=\\sqrt{p}u^p, \\quad v>0 \\quad in \\quad R^n \\end{array} \\right. $$ with $n \\geq 3$ and $p>1$. We investigate the existence and the nonexistence of positive classical solutions with the help of an integral system involving the Newton potential $$ \\left \\{ \\begin{array}{l} u(x)=c_1\\displaystyle\\int_{R^n}\\frac{u^{p-1}(y)v(y)dy}{|x-y|^{n-2}}, \\quad u>0 \\quad in \\quad R^n, v(x)=c_2\\displaystyle\\int_{R^n}\\frac{u^p(y)dy}{|x-y|^{n-2}} \\quad v>0 \\quad i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1523","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":"1411.1523","created_at":"2026-05-18T02:38:27.701848+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.1523v1","created_at":"2026-05-18T02:38:27.701848+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1523","created_at":"2026-05-18T02:38:27.701848+00:00"},{"alias_kind":"pith_short_12","alias_value":"J52NXNP7RMFI","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"J52NXNP7RMFIR63P","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"J52NXNP7","created_at":"2026-05-18T12:28:33.132498+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/J52NXNP7RMFIR63PYPPPMSCDH7","json":"https://pith.science/pith/J52NXNP7RMFIR63PYPPPMSCDH7.json","graph_json":"https://pith.science/api/pith-number/J52NXNP7RMFIR63PYPPPMSCDH7/graph.json","events_json":"https://pith.science/api/pith-number/J52NXNP7RMFIR63PYPPPMSCDH7/events.json","paper":"https://pith.science/paper/J52NXNP7"},"agent_actions":{"view_html":"https://pith.science/pith/J52NXNP7RMFIR63PYPPPMSCDH7","download_json":"https://pith.science/pith/J52NXNP7RMFIR63PYPPPMSCDH7.json","view_paper":"https://pith.science/paper/J52NXNP7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.1523&json=true","fetch_graph":"https://pith.science/api/pith-number/J52NXNP7RMFIR63PYPPPMSCDH7/graph.json","fetch_events":"https://pith.science/api/pith-number/J52NXNP7RMFIR63PYPPPMSCDH7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J52NXNP7RMFIR63PYPPPMSCDH7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J52NXNP7RMFIR63PYPPPMSCDH7/action/storage_attestation","attest_author":"https://pith.science/pith/J52NXNP7RMFIR63PYPPPMSCDH7/action/author_attestation","sign_citation":"https://pith.science/pith/J52NXNP7RMFIR63PYPPPMSCDH7/action/citation_signature","submit_replication":"https://pith.science/pith/J52NXNP7RMFIR63PYPPPMSCDH7/action/replication_record"}},"created_at":"2026-05-18T02:38:27.701848+00:00","updated_at":"2026-05-18T02:38:27.701848+00:00"}