{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3APB4FE3XLHBWNWIHLQ6TJTSRH","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7254c69fee9da924deef5dbfc027d67d869dcfeb618dc6218039a8689ae58e64","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-15T19:02:15Z","title_canon_sha256":"96b15bda65491b03db84a6dc73b84c1fc0117a856367ad8b1183a6375f172b20"},"schema_version":"1.0","source":{"id":"1412.4722","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4722","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4722v2","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4722","created_at":"2026-05-18T01:02:14Z"},{"alias_kind":"pith_short_12","alias_value":"3APB4FE3XLHB","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3APB4FE3XLHBWNWI","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3APB4FE3","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:0e6be80816426eaae30ef0f349b754f3026841971272391608c134dee069a342","target":"graph","created_at":"2026-05-18T01:02:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove the existence of an unbounded branch of solutions to the non-linear non-local equation $$ (-\\Delta)^s_p u=\\lambda |u|^{p-2}u + f(x,u,\\lambda) \\quad\\text{in}\\quad \\Omega,\\quad u=0 \\quad\\text{in}\\quad \\mathbb{R}^n\\setminus\\Omega, $$ bifurcating from the first eigenvalue. Here $(-\\Delta)^s_p$ denotes the fractional $p$-Laplacian and $\\Omega\\subset\\mathbb{R}^n$ is a bounded regular domain. The proof of the bifurcation results relies in computing the Leray--Schauder degree by making an homotopy respect to $s$ (the order of the fractional $p$-Laplacian) and then to use results of local case","authors_text":"Alexander Quaas, Leandro M. Del Pezzo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-15T19:02:15Z","title":"Global bifurcation for fractional $p$-Laplacian and application"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4722","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f9f73615ebd89ac7eba44813b89e9ce104e36715fac8fb08eb5f12c03a187c3f","target":"record","created_at":"2026-05-18T01:02:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7254c69fee9da924deef5dbfc027d67d869dcfeb618dc6218039a8689ae58e64","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-15T19:02:15Z","title_canon_sha256":"96b15bda65491b03db84a6dc73b84c1fc0117a856367ad8b1183a6375f172b20"},"schema_version":"1.0","source":{"id":"1412.4722","kind":"arxiv","version":2}},"canonical_sha256":"d81e1e149bbace1b36c83ae1e9a67289e35b3174783cc7452223c91d3df4035e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d81e1e149bbace1b36c83ae1e9a67289e35b3174783cc7452223c91d3df4035e","first_computed_at":"2026-05-18T01:02:14.056264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:14.056264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OzXvgaUOdqmjqoY+iojPDCXuJt3hwDB8QuMdocCpMag3RbF0EiRewCh3XCpH164X+6GxwwylDjcl89r2m6V8AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:14.056985Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.4722","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9f73615ebd89ac7eba44813b89e9ce104e36715fac8fb08eb5f12c03a187c3f","sha256:0e6be80816426eaae30ef0f349b754f3026841971272391608c134dee069a342"],"state_sha256":"8872fea7c1e4509251d5e8bdb55101ccb4cbf521d58ceb631d5d8e502b368278"}