{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ODVUBL4253JD3ADDT3MRBVVMUR","short_pith_number":"pith:ODVUBL42","schema_version":"1.0","canonical_sha256":"70eb40af9aeed23d80639ed910d6aca443617a7fadba9dbd89377da0ad733d61","source":{"kind":"arxiv","id":"1610.09062","version":2},"attestation_state":"computed","paper":{"title":"Isolated singularities of positive solutions for Choquard equations in sublinear case","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Feng Zhou, Huyuan Chen","submitted_at":"2016-10-28T02:45:40Z","abstract_excerpt":"Our purpose of this paper is to study the isolated singularities of positive solutions to Choquard equation in the sublinear case $q \\in (0,1)$\n  $$\\displaystyle \\ \\ -\\Delta u+ u =I_\\alpha[u^p] u^q\\;\\;\n  {\\rm in}\\; \\mathbb{R}^N\\setminus\\{0\\},\n  % [2mm] \\phantom{ }\n  \\;\\; \\displaystyle \\lim_{|x|\\to+\\infty}u(x)=0, $$ where $p >0, N \\geq 3, \\alpha \\in (0,N)$ and $I_{\\alpha}[u^p](x) = \\int_{\\mathbb{R}^N} \\frac{u^p(y)}{|x-y|^{N-\\alpha}}dy$ is the Riesz potential, which appears as a nonlocal term in the equation. We investigate the nonexistence and existence of isolated singular solutions of Choquar"},"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":"1610.09062","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2016-10-28T02:45:40Z","cross_cats_sorted":[],"title_canon_sha256":"396b4542016cdbc7a947b2ead7e4b3fffb87628af6d1ef4768bcd0b40bebeccc","abstract_canon_sha256":"863033c6018298cf213138261796c7cd0f947028f76e7b5eca728e40ba8a6103"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:23.561301Z","signature_b64":"zCNRr4sbTWRyUhobw8RCLe4+mhRuw7STd/2yXSQwH8zeSyPwmiPLDlqIOy1QMbBPVHzp90Lv/ndIuhM6L/IpCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70eb40af9aeed23d80639ed910d6aca443617a7fadba9dbd89377da0ad733d61","last_reissued_at":"2026-05-18T00:49:23.560876Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:23.560876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isolated singularities of positive solutions for Choquard equations in sublinear case","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Feng Zhou, Huyuan Chen","submitted_at":"2016-10-28T02:45:40Z","abstract_excerpt":"Our purpose of this paper is to study the isolated singularities of positive solutions to Choquard equation in the sublinear case $q \\in (0,1)$\n  $$\\displaystyle \\ \\ -\\Delta u+ u =I_\\alpha[u^p] u^q\\;\\;\n  {\\rm in}\\; \\mathbb{R}^N\\setminus\\{0\\},\n  % [2mm] \\phantom{ }\n  \\;\\; \\displaystyle \\lim_{|x|\\to+\\infty}u(x)=0, $$ where $p >0, N \\geq 3, \\alpha \\in (0,N)$ and $I_{\\alpha}[u^p](x) = \\int_{\\mathbb{R}^N} \\frac{u^p(y)}{|x-y|^{N-\\alpha}}dy$ is the Riesz potential, which appears as a nonlocal term in the equation. 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