{"paper":{"title":"Existence of three solutions for a first-order problem with nonlinear non-local boundary conditions","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Douglas R. Anderson","submitted_at":"2012-07-20T19:56:40Z","abstract_excerpt":"Conditions for the existence of at least three positive solutions to the nonlinear first-order problem with a nonlinear nonlocal boundary condition given by\n  && y'(t) - p(t)y(t) = \\sum_{i=1}^m f_i\\big(t,y(t)\\big), \\quad t\\in[0,1],\n  && \\lambda y(0) = y(1) + \\sum_{j=1}^n \\Phi_j(\\tau_j,y(\\tau_j)), \\quad \\tau_j\\in[0,1],\nare discussed, for sufficiently large $\\lambda>1$. The Leggett-Williams fixed point theorem is utilized."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5039","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"}