{"paper":{"title":"Linear, 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":"2011-06-23T15:00:04Z","abstract_excerpt":"We consider the linear eigenvalue problem \\tag{1}\n  -u\" = \\lambda u, \\quad \\text{on $(-1,1)$}, where $\\lambda \\in \\mathbb{R}$, together with the general multi-point boundary conditions \\tag{2} \\alpha_0^\\pm u(\\pm 1) + \\beta_0^\\pm u'(\\pm 1) = \\sum^{m^\\pm}_{i=1} \\alpha^\\pm_i u(\\eta^\\pm_i)\n  + \\sum_{i=1}^{m^\\pm} \\beta^\\pm_i u'(\\eta^\\pm_i). We also suppose that: \\alpha_0^\\pm \\ge 0, \\quad \\alpha_0^\\pm + |\\beta_0^\\pm| > 0, \\tag{3}  \\pm \\beta_0^\\pm \\ge 0, \\tag{4} (\\frac{\\sum_{i=1}^{m^\\pm} |\\alpha_i^\\pm|}{\\alpha_0^\\pm})^2\n  + (\\frac{\\sum_{i=1}^{m^\\pm} |\\beta_i^\\pm|}{\\beta_0^\\pm})^2\n  < 1, \\tag{5} with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4747","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"}