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Rynne, Francois Genoud","submitted_at":"2011-10-04T15:01:59Z","abstract_excerpt":"We consider the nonlinear boundary value problem consisting of the equation\n\\tag{1} -u\" = f(u) + h, \\quad \\text{a.e. on $(-1,1)$,}\nwhere $h \\in L^1(-1,1)$, together with the multi-point, Dirichlet-type boundary conditions\n\\tag{2} u(\\pm 1) = \\sum^{m^\\pm}_{i=1}\\alpha^\\pm_i u(\\eta^\\pm_i)\nwhere $m^\\pm \\ge 1$ are integers, $\\alpha^\\pm = (\\alpha_1^\\pm, ...,\\alpha_m^\\pm) \\in [0,1)^{m^\\pm}$, $\\eta^\\pm \\in (-1,1)^{m^\\pm}$, and we suppose that $$\n  \\sum_{i=1}^{m^\\pm} \\alpha_i^\\pm < 1 . $$ We also suppose that $f : \\mathbb{R} \\to \\mathbb{R}$ is continuous, and $$ 0 < f_{\\pm\\infty}:=\\lim_{s \\to \\pm\\infty}"},"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":"1110.0712","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-04T15:01:59Z","cross_cats_sorted":[],"title_canon_sha256":"b4ea15ecdf8ba02923f415992ef2c30aeec105d2e21a167f2e0adcf7f6b479ab","abstract_canon_sha256":"d5bbc9fdb04848acc52ce2c7687fbb546e5ebfa1946c34832140f28c8b7c7a73"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:25.782418Z","signature_b64":"MFUmxRXIbvKr8GavCEwLKs1qgKN0UuurOksnbzhxKwP4cn+tZMyjHjE+H4rTMF3BEOP+qM7D2zwhsXZwneQkBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2095265072a1655d9015a07f53f093ddc0d916694c709b236299854f62948c4","last_reissued_at":"2026-05-18T03:40:25.781724Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:25.781724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Half eigenvalues and the Fucik spectrum of multi-point, boundary value problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bryan P. Rynne, Francois Genoud","submitted_at":"2011-10-04T15:01:59Z","abstract_excerpt":"We consider the nonlinear boundary value problem consisting of the equation\n\\tag{1} -u\" = f(u) + h, \\quad \\text{a.e. on $(-1,1)$,}\nwhere $h \\in L^1(-1,1)$, together with the multi-point, Dirichlet-type boundary conditions\n\\tag{2} u(\\pm 1) = \\sum^{m^\\pm}_{i=1}\\alpha^\\pm_i u(\\eta^\\pm_i)\nwhere $m^\\pm \\ge 1$ are integers, $\\alpha^\\pm = (\\alpha_1^\\pm, ...,\\alpha_m^\\pm) \\in [0,1)^{m^\\pm}$, $\\eta^\\pm \\in (-1,1)^{m^\\pm}$, and we suppose that $$\n  \\sum_{i=1}^{m^\\pm} \\alpha_i^\\pm < 1 . $$ We also suppose that $f : \\mathbb{R} \\to \\mathbb{R}$ is continuous, and $$ 0 < f_{\\pm\\infty}:=\\lim_{s \\to \\pm\\infty}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0712","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":"1110.0712","created_at":"2026-05-18T03:40:25.781811+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.0712v1","created_at":"2026-05-18T03:40:25.781811+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0712","created_at":"2026-05-18T03:40:25.781811+00:00"},{"alias_kind":"pith_short_12","alias_value":"2IEVEZIHFILF","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"2IEVEZIHFILFLWIB","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"2IEVEZIH","created_at":"2026-05-18T12:26:18.847500+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/2IEVEZIHFILFLWIBLID7KPYJHX","json":"https://pith.science/pith/2IEVEZIHFILFLWIBLID7KPYJHX.json","graph_json":"https://pith.science/api/pith-number/2IEVEZIHFILFLWIBLID7KPYJHX/graph.json","events_json":"https://pith.science/api/pith-number/2IEVEZIHFILFLWIBLID7KPYJHX/events.json","paper":"https://pith.science/paper/2IEVEZIH"},"agent_actions":{"view_html":"https://pith.science/pith/2IEVEZIHFILFLWIBLID7KPYJHX","download_json":"https://pith.science/pith/2IEVEZIHFILFLWIBLID7KPYJHX.json","view_paper":"https://pith.science/paper/2IEVEZIH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.0712&json=true","fetch_graph":"https://pith.science/api/pith-number/2IEVEZIHFILFLWIBLID7KPYJHX/graph.json","fetch_events":"https://pith.science/api/pith-number/2IEVEZIHFILFLWIBLID7KPYJHX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2IEVEZIHFILFLWIBLID7KPYJHX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2IEVEZIHFILFLWIBLID7KPYJHX/action/storage_attestation","attest_author":"https://pith.science/pith/2IEVEZIHFILFLWIBLID7KPYJHX/action/author_attestation","sign_citation":"https://pith.science/pith/2IEVEZIHFILFLWIBLID7KPYJHX/action/citation_signature","submit_replication":"https://pith.science/pith/2IEVEZIHFILFLWIBLID7KPYJHX/action/replication_record"}},"created_at":"2026-05-18T03:40:25.781811+00:00","updated_at":"2026-05-18T03:40:25.781811+00:00"}