{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZXGBWTBCME5DWUNMB4GXSRQHF6","short_pith_number":"pith:ZXGBWTBC","schema_version":"1.0","canonical_sha256":"cdcc1b4c22613a3b51ac0f0d7946072f814e087af8d22a6e1c969357f340db8f","source":{"kind":"arxiv","id":"1309.7142","version":2},"attestation_state":"computed","paper":{"title":"Multiplicity of normalized solutions for a class of nonlinear Schrodinger-Poisson-Slater equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tingjian Luo","submitted_at":"2013-09-27T08:18:29Z","abstract_excerpt":"In this paper, we prove a multiplicity result of solutions for the following stationary Schr\\\"odinger-Poisson-Slater equations \\begin{equation}\\label{eq-abstract} -\\Delta u - \\lambda u + (\\left | x \\right |^{-1}\\ast \\left | u \\right |^2) u - |u|^{p-2}u = 0 \\ \\mbox{ in } \\ \\mathbb{R}^{3}, \\end{equation} where $\\lambda\\in \\R$ is a parameter, and $p\\in (2,6)$. The solutions we obtained have a prescribed $L^2$-norm. Our proofs are mainly inspired by a recent work of Bartsch and De Valeriola [7]."},"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":"1309.7142","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-27T08:18:29Z","cross_cats_sorted":[],"title_canon_sha256":"b4cd599085529526c711906c77c0050162d019a1daf69933cfa34d6359595ab2","abstract_canon_sha256":"4b3c556328c643665529000b9d65a64d46b053efc288660127766a2baf061daf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:58.472948Z","signature_b64":"KjtwPYNFXfvGnhKe8RqKFAanyPs1ay84/YDgj+ghJ6eGqJidAfGTSPdhKEGUcgrYmtxsqnzhZKMVU7PSTqM1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdcc1b4c22613a3b51ac0f0d7946072f814e087af8d22a6e1c969357f340db8f","last_reissued_at":"2026-05-18T03:08:58.472448Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:58.472448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiplicity of normalized solutions for a class of nonlinear Schrodinger-Poisson-Slater equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tingjian Luo","submitted_at":"2013-09-27T08:18:29Z","abstract_excerpt":"In this paper, we prove a multiplicity result of solutions for the following stationary Schr\\\"odinger-Poisson-Slater equations \\begin{equation}\\label{eq-abstract} -\\Delta u - \\lambda u + (\\left | x \\right |^{-1}\\ast \\left | u \\right |^2) u - |u|^{p-2}u = 0 \\ \\mbox{ in } \\ \\mathbb{R}^{3}, \\end{equation} where $\\lambda\\in \\R$ is a parameter, and $p\\in (2,6)$. The solutions we obtained have a prescribed $L^2$-norm. Our proofs are mainly inspired by a recent work of Bartsch and De Valeriola [7]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7142","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":"1309.7142","created_at":"2026-05-18T03:08:58.472523+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.7142v2","created_at":"2026-05-18T03:08:58.472523+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7142","created_at":"2026-05-18T03:08:58.472523+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZXGBWTBCME5D","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZXGBWTBCME5DWUNM","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZXGBWTBC","created_at":"2026-05-18T12:28:09.283467+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/ZXGBWTBCME5DWUNMB4GXSRQHF6","json":"https://pith.science/pith/ZXGBWTBCME5DWUNMB4GXSRQHF6.json","graph_json":"https://pith.science/api/pith-number/ZXGBWTBCME5DWUNMB4GXSRQHF6/graph.json","events_json":"https://pith.science/api/pith-number/ZXGBWTBCME5DWUNMB4GXSRQHF6/events.json","paper":"https://pith.science/paper/ZXGBWTBC"},"agent_actions":{"view_html":"https://pith.science/pith/ZXGBWTBCME5DWUNMB4GXSRQHF6","download_json":"https://pith.science/pith/ZXGBWTBCME5DWUNMB4GXSRQHF6.json","view_paper":"https://pith.science/paper/ZXGBWTBC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.7142&json=true","fetch_graph":"https://pith.science/api/pith-number/ZXGBWTBCME5DWUNMB4GXSRQHF6/graph.json","fetch_events":"https://pith.science/api/pith-number/ZXGBWTBCME5DWUNMB4GXSRQHF6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZXGBWTBCME5DWUNMB4GXSRQHF6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZXGBWTBCME5DWUNMB4GXSRQHF6/action/storage_attestation","attest_author":"https://pith.science/pith/ZXGBWTBCME5DWUNMB4GXSRQHF6/action/author_attestation","sign_citation":"https://pith.science/pith/ZXGBWTBCME5DWUNMB4GXSRQHF6/action/citation_signature","submit_replication":"https://pith.science/pith/ZXGBWTBCME5DWUNMB4GXSRQHF6/action/replication_record"}},"created_at":"2026-05-18T03:08:58.472523+00:00","updated_at":"2026-05-18T03:08:58.472523+00:00"}