{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FZB52HPVW55H255K3KIJY65KV7","short_pith_number":"pith:FZB52HPV","schema_version":"1.0","canonical_sha256":"2e43dd1df5b77a7d77aada909c7baaaffc56c54856d506f6cdbb3ec6e13fe4bb","source":{"kind":"arxiv","id":"1502.05927","version":2},"attestation_state":"computed","paper":{"title":"Infinitely many global continua bifurcating from a single solution of an elliptic problem with concave-convex nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rainer Mandel, Thomas Bartsch","submitted_at":"2015-02-20T16:43:12Z","abstract_excerpt":"We study the bifurcation of solutions of semilinear elliptic boundary value problems of the form \\begin{align*}\n  \\begin{aligned}\n  -\\Delta u &= f_\\lambda(|x|,u,|\\nabla u|) &&\\text{in }\\Omega,\n  u &= 0 &&\\text{on }\\partial\\Omega,\n  \\end{aligned} \\end{align*} on an annulus $\\Omega\\subset\\mathbb{R}^N$, with a concave-convex nonlinearity, a special case being the nonlinearity first considered by Ambrosetti, Brezis and Cerami: $f_\\lambda(|x|,u,|\\nabla u|)=\\lambda|u|^{q-2}u + |u|^{p-2}u$ with $1<q<2<p$. Although the trivial solution $u_0\\equiv0$ is nondegenerate if $\\lambda=0$ we prove that $(\\lamb"},"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":"1502.05927","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-20T16:43:12Z","cross_cats_sorted":[],"title_canon_sha256":"5e189adf69377732b4ccf3be313d5e7530ac3c533bfdd31ea1e6f0777b82346c","abstract_canon_sha256":"946484dd06efff78337e2344b547810b34cceece517b174d9ad42cc2f4c7b486"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:18.985461Z","signature_b64":"BEKo9j1r3AN/2JOR2xc3mfm2Lt2Yg0Cqo1WVMus8sUVm7wD+wdthkuPkqtqlR35ytzocLRlf5dGOnruUIO9iCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e43dd1df5b77a7d77aada909c7baaaffc56c54856d506f6cdbb3ec6e13fe4bb","last_reissued_at":"2026-05-18T01:23:18.984763Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:18.984763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinitely many global continua bifurcating from a single solution of an elliptic problem with concave-convex nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rainer Mandel, Thomas Bartsch","submitted_at":"2015-02-20T16:43:12Z","abstract_excerpt":"We study the bifurcation of solutions of semilinear elliptic boundary value problems of the form \\begin{align*}\n  \\begin{aligned}\n  -\\Delta u &= f_\\lambda(|x|,u,|\\nabla u|) &&\\text{in }\\Omega,\n  u &= 0 &&\\text{on }\\partial\\Omega,\n  \\end{aligned} \\end{align*} on an annulus $\\Omega\\subset\\mathbb{R}^N$, with a concave-convex nonlinearity, a special case being the nonlinearity first considered by Ambrosetti, Brezis and Cerami: $f_\\lambda(|x|,u,|\\nabla u|)=\\lambda|u|^{q-2}u + |u|^{p-2}u$ with $1<q<2<p$. Although the trivial solution $u_0\\equiv0$ is nondegenerate if $\\lambda=0$ we prove that $(\\lamb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05927","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":"1502.05927","created_at":"2026-05-18T01:23:18.984856+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.05927v2","created_at":"2026-05-18T01:23:18.984856+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05927","created_at":"2026-05-18T01:23:18.984856+00:00"},{"alias_kind":"pith_short_12","alias_value":"FZB52HPVW55H","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"FZB52HPVW55H255K","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"FZB52HPV","created_at":"2026-05-18T12:29:22.688609+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/FZB52HPVW55H255K3KIJY65KV7","json":"https://pith.science/pith/FZB52HPVW55H255K3KIJY65KV7.json","graph_json":"https://pith.science/api/pith-number/FZB52HPVW55H255K3KIJY65KV7/graph.json","events_json":"https://pith.science/api/pith-number/FZB52HPVW55H255K3KIJY65KV7/events.json","paper":"https://pith.science/paper/FZB52HPV"},"agent_actions":{"view_html":"https://pith.science/pith/FZB52HPVW55H255K3KIJY65KV7","download_json":"https://pith.science/pith/FZB52HPVW55H255K3KIJY65KV7.json","view_paper":"https://pith.science/paper/FZB52HPV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.05927&json=true","fetch_graph":"https://pith.science/api/pith-number/FZB52HPVW55H255K3KIJY65KV7/graph.json","fetch_events":"https://pith.science/api/pith-number/FZB52HPVW55H255K3KIJY65KV7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FZB52HPVW55H255K3KIJY65KV7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FZB52HPVW55H255K3KIJY65KV7/action/storage_attestation","attest_author":"https://pith.science/pith/FZB52HPVW55H255K3KIJY65KV7/action/author_attestation","sign_citation":"https://pith.science/pith/FZB52HPVW55H255K3KIJY65KV7/action/citation_signature","submit_replication":"https://pith.science/pith/FZB52HPVW55H255K3KIJY65KV7/action/replication_record"}},"created_at":"2026-05-18T01:23:18.984856+00:00","updated_at":"2026-05-18T01:23:18.984856+00:00"}