{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:R5OA4NF3TSB76QX25PEH4MUN4C","short_pith_number":"pith:R5OA4NF3","schema_version":"1.0","canonical_sha256":"8f5c0e34bb9c83ff42faebc87e328de0bf1324a91c0e54a80de404aac2a01c58","source":{"kind":"arxiv","id":"1602.06102","version":1},"attestation_state":"computed","paper":{"title":"Two-bubble nodal solutions for slightly subcritical Fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qianqiao Guo, Yunyun Hu","submitted_at":"2016-02-19T10:26:31Z","abstract_excerpt":"In this paper, we consider the existence of nodal solutions with two bubbles to the slightly subcritical problem with the fractional Laplacian \\begin{equation*} \\left\\{\\aligned &(-\\Delta)^su=|u|^{p-1-\\varepsilon}u\\ \\ \\mbox{in}\\ \\Omega &u=0\\ \\mbox{on}\\ \\partial\\Omega, \\endaligned \\right. \\end{equation*} where $\\Omega$ is a smooth bounded domain in $\\mathbb R^N$, $N>2s$, $0<s<1$, $ p=\\frac{N+2s}{N-2s}$ and $\\varepsilon>0$ is a small parameter, which can be seen as a nonlocal analog of the results of Bartsch, Micheletti and Pistoia (2006) \\cite{Bartsch1}."},"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":"1602.06102","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-19T10:26:31Z","cross_cats_sorted":[],"title_canon_sha256":"ffd91d28e308eb8af026be69657c7c6417d22cca1abe69ea0418f8872380a4ee","abstract_canon_sha256":"23f085772dcc584b2451d7b9da382cde10a938fdd7c3faa6952a677fb3661045"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:21.590548Z","signature_b64":"qMHjOJdbyHCXiM2UGlR4auDeldyQP3ak1KyNHALMUCcuDV/bLSqCp9ZqQnSG3G4PTlcYzPezjWnjxtimtK0BBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f5c0e34bb9c83ff42faebc87e328de0bf1324a91c0e54a80de404aac2a01c58","last_reissued_at":"2026-05-18T01:20:21.590070Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:21.590070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two-bubble nodal solutions for slightly subcritical Fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qianqiao Guo, Yunyun Hu","submitted_at":"2016-02-19T10:26:31Z","abstract_excerpt":"In this paper, we consider the existence of nodal solutions with two bubbles to the slightly subcritical problem with the fractional Laplacian \\begin{equation*} \\left\\{\\aligned &(-\\Delta)^su=|u|^{p-1-\\varepsilon}u\\ \\ \\mbox{in}\\ \\Omega &u=0\\ \\mbox{on}\\ \\partial\\Omega, \\endaligned \\right. \\end{equation*} where $\\Omega$ is a smooth bounded domain in $\\mathbb R^N$, $N>2s$, $0<s<1$, $ p=\\frac{N+2s}{N-2s}$ and $\\varepsilon>0$ is a small parameter, which can be seen as a nonlocal analog of the results of Bartsch, Micheletti and Pistoia (2006) \\cite{Bartsch1}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06102","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":"1602.06102","created_at":"2026-05-18T01:20:21.590140+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.06102v1","created_at":"2026-05-18T01:20:21.590140+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06102","created_at":"2026-05-18T01:20:21.590140+00:00"},{"alias_kind":"pith_short_12","alias_value":"R5OA4NF3TSB7","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_16","alias_value":"R5OA4NF3TSB76QX2","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_8","alias_value":"R5OA4NF3","created_at":"2026-05-18T12:30:41.710351+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/R5OA4NF3TSB76QX25PEH4MUN4C","json":"https://pith.science/pith/R5OA4NF3TSB76QX25PEH4MUN4C.json","graph_json":"https://pith.science/api/pith-number/R5OA4NF3TSB76QX25PEH4MUN4C/graph.json","events_json":"https://pith.science/api/pith-number/R5OA4NF3TSB76QX25PEH4MUN4C/events.json","paper":"https://pith.science/paper/R5OA4NF3"},"agent_actions":{"view_html":"https://pith.science/pith/R5OA4NF3TSB76QX25PEH4MUN4C","download_json":"https://pith.science/pith/R5OA4NF3TSB76QX25PEH4MUN4C.json","view_paper":"https://pith.science/paper/R5OA4NF3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.06102&json=true","fetch_graph":"https://pith.science/api/pith-number/R5OA4NF3TSB76QX25PEH4MUN4C/graph.json","fetch_events":"https://pith.science/api/pith-number/R5OA4NF3TSB76QX25PEH4MUN4C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R5OA4NF3TSB76QX25PEH4MUN4C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R5OA4NF3TSB76QX25PEH4MUN4C/action/storage_attestation","attest_author":"https://pith.science/pith/R5OA4NF3TSB76QX25PEH4MUN4C/action/author_attestation","sign_citation":"https://pith.science/pith/R5OA4NF3TSB76QX25PEH4MUN4C/action/citation_signature","submit_replication":"https://pith.science/pith/R5OA4NF3TSB76QX25PEH4MUN4C/action/replication_record"}},"created_at":"2026-05-18T01:20:21.590140+00:00","updated_at":"2026-05-18T01:20:21.590140+00:00"}