{"paper":{"title":"Second order, multi-point problems with variable coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.CA","authors_text":"Bryan P. Rynne, Francois Genoud","submitted_at":"2011-06-20T15:17:07Z","abstract_excerpt":"In this paper we consider the eigenvalue problem consisting of the equation  -u\" = \\la r u, \\quad \\text{on $(-1,1)$}, where $r \\in C^1[-1,1], \\ r>0$ and $\\la \\in \\R$, together with the multi-point boundary conditions u(\\pm 1) = \\sum^{m^\\pm}_{i=1} \\al^\\pm_i u(\\eta^\\pm_i), where $m^\\pm \\ge 1$ are integers, and, for $i = 1,...,m^\\pm$, $\\al_i^\\pm \\in \\R$, $\\eta_i^\\pm \\in [-1,1]$, with $\\eta_i^+ \\ne 1$, $\\eta_i^- \\ne -1$. We show that if the coefficients $\\al_i^\\pm \\in \\R$ are sufficiently small (depending on $r$) then the spectral properties of this problem are similar to those of the usual separa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3936","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"}