{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UFGVPNZGR3XJUIHMF6ET6J7PKD","short_pith_number":"pith:UFGVPNZG","schema_version":"1.0","canonical_sha256":"a14d57b7268eee9a20ec2f893f27ef50d6eb6fe02ccfbc9510b57ab8e5fb0eb4","source":{"kind":"arxiv","id":"1804.01687","version":1},"attestation_state":"computed","paper":{"title":"Infinitely many non-radial solutions to a critical equation on annulus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Benniao Li, Shusen Yan, Yuxia Guo","submitted_at":"2018-04-05T06:55:47Z","abstract_excerpt":"In this paper, we build infinitely many non-radial sign-changing solutions to the critical problem: \\begin{equation*} \\left\\{\\begin{array}{rlll} -\\Delta u&=|u|^{\\frac{4}{N-2}}u, &\\hbox{ in }\\Omega,\\\\ u&=0, &\\hbox{ on }\\partial\\Omega. \\end{array}\\right. \\eqno(P) \\end{equation*} on the annulus $\\Omega:=\\{x\\in \\mathbb{R}^N: a<|x|<b\\}$, $N\\geq 3.$ In particular, for any integer $k$ large enough, we build a non-radial solution which look like the unique positive solution $u_0$ to $(P)$ crowned by $k$ negative bubbles arranged on a regular polygon with radius $r_0$ such that $r_0^{\\frac{N-2}{2}}u_0("},"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":"1804.01687","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-05T06:55:47Z","cross_cats_sorted":[],"title_canon_sha256":"31d0b9474693c4cf5b94a969c4c775a5b35708d65d663276b964a50ca69943b1","abstract_canon_sha256":"c6c0fc0ec18c300a5eaa8cdcd42657f6d22d9ea50440e08b68e67df6e76db7fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:10.361006Z","signature_b64":"Q58wSRbdTjnLiEv9PutBvDggcIvetxueimz+K5zuv+GlkS9fH2P6AZV1a8CX4DMcMVR1/Co+SLrGHl8wWGEkBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a14d57b7268eee9a20ec2f893f27ef50d6eb6fe02ccfbc9510b57ab8e5fb0eb4","last_reissued_at":"2026-05-18T00:19:10.360534Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:10.360534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinitely many non-radial solutions to a critical equation on annulus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angela Pistoia, Benniao Li, Shusen Yan, Yuxia Guo","submitted_at":"2018-04-05T06:55:47Z","abstract_excerpt":"In this paper, we build infinitely many non-radial sign-changing solutions to the critical problem: \\begin{equation*} \\left\\{\\begin{array}{rlll} -\\Delta u&=|u|^{\\frac{4}{N-2}}u, &\\hbox{ in }\\Omega,\\\\ u&=0, &\\hbox{ on }\\partial\\Omega. \\end{array}\\right. \\eqno(P) \\end{equation*} on the annulus $\\Omega:=\\{x\\in \\mathbb{R}^N: a<|x|<b\\}$, $N\\geq 3.$ In particular, for any integer $k$ large enough, we build a non-radial solution which look like the unique positive solution $u_0$ to $(P)$ crowned by $k$ negative bubbles arranged on a regular polygon with radius $r_0$ such that $r_0^{\\frac{N-2}{2}}u_0("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01687","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":"1804.01687","created_at":"2026-05-18T00:19:10.360603+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.01687v1","created_at":"2026-05-18T00:19:10.360603+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01687","created_at":"2026-05-18T00:19:10.360603+00:00"},{"alias_kind":"pith_short_12","alias_value":"UFGVPNZGR3XJ","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"UFGVPNZGR3XJUIHM","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"UFGVPNZG","created_at":"2026-05-18T12:32:56.356000+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/UFGVPNZGR3XJUIHMF6ET6J7PKD","json":"https://pith.science/pith/UFGVPNZGR3XJUIHMF6ET6J7PKD.json","graph_json":"https://pith.science/api/pith-number/UFGVPNZGR3XJUIHMF6ET6J7PKD/graph.json","events_json":"https://pith.science/api/pith-number/UFGVPNZGR3XJUIHMF6ET6J7PKD/events.json","paper":"https://pith.science/paper/UFGVPNZG"},"agent_actions":{"view_html":"https://pith.science/pith/UFGVPNZGR3XJUIHMF6ET6J7PKD","download_json":"https://pith.science/pith/UFGVPNZGR3XJUIHMF6ET6J7PKD.json","view_paper":"https://pith.science/paper/UFGVPNZG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.01687&json=true","fetch_graph":"https://pith.science/api/pith-number/UFGVPNZGR3XJUIHMF6ET6J7PKD/graph.json","fetch_events":"https://pith.science/api/pith-number/UFGVPNZGR3XJUIHMF6ET6J7PKD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UFGVPNZGR3XJUIHMF6ET6J7PKD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UFGVPNZGR3XJUIHMF6ET6J7PKD/action/storage_attestation","attest_author":"https://pith.science/pith/UFGVPNZGR3XJUIHMF6ET6J7PKD/action/author_attestation","sign_citation":"https://pith.science/pith/UFGVPNZGR3XJUIHMF6ET6J7PKD/action/citation_signature","submit_replication":"https://pith.science/pith/UFGVPNZGR3XJUIHMF6ET6J7PKD/action/replication_record"}},"created_at":"2026-05-18T00:19:10.360603+00:00","updated_at":"2026-05-18T00:19:10.360603+00:00"}