{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:YPALHATMLG4Q6E7GOCFDA565AG","short_pith_number":"pith:YPALHATM","schema_version":"1.0","canonical_sha256":"c3c0b3826c59b90f13e6708a3077dd01a4ea91c239739fc738dfff7bfde33f3c","source":{"kind":"arxiv","id":"1609.07273","version":2},"attestation_state":"computed","paper":{"title":"Positive solutions for nonlinear Choquard equation with singular nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Konijeti Sreenadh, Tuhina Mukherjee","submitted_at":"2016-09-23T08:51:47Z","abstract_excerpt":"In this article, we study the following nonlinear Choquard equation with singular nonlinearity \\begin{equation*}\n  \\quad -\\De u = \\la u^{-q} + \\left( \\int_{\\Om}\\frac{|u|^{2^*_{\\mu}}}{|x-y|^{\\mu}}\\mathrm{d}y \\right)|u|^{2^*_{\\mu}-2}u, \\quad u>0 \\; \\text{in}\\; \\Om,\\quad u = 0 \\; \\mbox{on}\\; \\partial\\Om, \\end{equation*} where $\\Om$ is a bounded domain in $\\mb{R}^n$ with smooth boundary $\\partial \\Om$, $n > 2,\\; \\la >0,\\; 0 < q < 1, \\; 0<\\mu<n$ and $2^*_\\mu=\\frac{2n-\\mu}{n-2}$. Using variational approach and structure of associated Nehari manifold, we show the existence and multiplicity of positiv"},"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":"1609.07273","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-23T08:51:47Z","cross_cats_sorted":[],"title_canon_sha256":"a21e16ee7d7bb020acf02e5478c8cd078e894732dc5ee4f47f564554add65516","abstract_canon_sha256":"00b7b8c43c1c1731c1cd965e1302360ad1d080fbfd11ffd18cda12173d2b46d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:33.472359Z","signature_b64":"5o3sK7Q6jdYP9jUh4OpwcPQ80srBQBsN11hE9qYltU9ADLR0nJ//5hrXdt8ajGodA3+rNDBiZNO041gZtNDvDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3c0b3826c59b90f13e6708a3077dd01a4ea91c239739fc738dfff7bfde33f3c","last_reissued_at":"2026-05-18T01:00:33.471743Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:33.471743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Positive solutions for nonlinear Choquard equation with singular nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Konijeti Sreenadh, Tuhina Mukherjee","submitted_at":"2016-09-23T08:51:47Z","abstract_excerpt":"In this article, we study the following nonlinear Choquard equation with singular nonlinearity \\begin{equation*}\n  \\quad -\\De u = \\la u^{-q} + \\left( \\int_{\\Om}\\frac{|u|^{2^*_{\\mu}}}{|x-y|^{\\mu}}\\mathrm{d}y \\right)|u|^{2^*_{\\mu}-2}u, \\quad u>0 \\; \\text{in}\\; \\Om,\\quad u = 0 \\; \\mbox{on}\\; \\partial\\Om, \\end{equation*} where $\\Om$ is a bounded domain in $\\mb{R}^n$ with smooth boundary $\\partial \\Om$, $n > 2,\\; \\la >0,\\; 0 < q < 1, \\; 0<\\mu<n$ and $2^*_\\mu=\\frac{2n-\\mu}{n-2}$. Using variational approach and structure of associated Nehari manifold, we show the existence and multiplicity of positiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07273","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":"1609.07273","created_at":"2026-05-18T01:00:33.471849+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.07273v2","created_at":"2026-05-18T01:00:33.471849+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07273","created_at":"2026-05-18T01:00:33.471849+00:00"},{"alias_kind":"pith_short_12","alias_value":"YPALHATMLG4Q","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_16","alias_value":"YPALHATMLG4Q6E7G","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_8","alias_value":"YPALHATM","created_at":"2026-05-18T12:30:53.716459+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/YPALHATMLG4Q6E7GOCFDA565AG","json":"https://pith.science/pith/YPALHATMLG4Q6E7GOCFDA565AG.json","graph_json":"https://pith.science/api/pith-number/YPALHATMLG4Q6E7GOCFDA565AG/graph.json","events_json":"https://pith.science/api/pith-number/YPALHATMLG4Q6E7GOCFDA565AG/events.json","paper":"https://pith.science/paper/YPALHATM"},"agent_actions":{"view_html":"https://pith.science/pith/YPALHATMLG4Q6E7GOCFDA565AG","download_json":"https://pith.science/pith/YPALHATMLG4Q6E7GOCFDA565AG.json","view_paper":"https://pith.science/paper/YPALHATM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.07273&json=true","fetch_graph":"https://pith.science/api/pith-number/YPALHATMLG4Q6E7GOCFDA565AG/graph.json","fetch_events":"https://pith.science/api/pith-number/YPALHATMLG4Q6E7GOCFDA565AG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YPALHATMLG4Q6E7GOCFDA565AG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YPALHATMLG4Q6E7GOCFDA565AG/action/storage_attestation","attest_author":"https://pith.science/pith/YPALHATMLG4Q6E7GOCFDA565AG/action/author_attestation","sign_citation":"https://pith.science/pith/YPALHATMLG4Q6E7GOCFDA565AG/action/citation_signature","submit_replication":"https://pith.science/pith/YPALHATMLG4Q6E7GOCFDA565AG/action/replication_record"}},"created_at":"2026-05-18T01:00:33.471849+00:00","updated_at":"2026-05-18T01:00:33.471849+00:00"}