{"paper":{"title":"Linear and nonlinear, second-order problems with Sturm-Liouville-type, multi-point boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bryan P. Rynne","submitted_at":"2015-09-21T13:34:03Z","abstract_excerpt":"We consider the nonlinear equation $$-u'' = f(u) + h , \\quad \\text{on} \\quad (-1,1),$$ where $f : {\\mathbb R} \\to {\\mathbb R}$ and $h : [-1,1] \\to {\\mathbb R}$ are continuous, together with general Sturm-Liouville type, multi-point boundary conditions at $\\pm 1$. We will obtain existence of solutions of this boundary value problem under certain `nonresonance' conditions, and also Rabinowitz-type global bifurcation results, which yield nodal solutions of the problem.\n  These results rely on the spectral properties of the eigenvalue problem consisting of the equation $$-u'' = \\lambda u, \\quad \\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06221","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"}