{"paper":{"title":"Nonlinear scalar discrete multipoint boundary value problems at resonance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Daniel Maroncelli","submitted_at":"2018-11-15T16:56:17Z","abstract_excerpt":"In this work we provide conditions for the existence of solutions to nonlinear boundary value problems of the form \\begin{equation*} y(t+n)+a_{n-1}(t)y(t+n-1)+\\cdots a_0(t)y(t)=g(t,y(t+m-1)) \\end{equation*} subject to \\begin{equation*} \\sum_{j=1}^nb_{ij}(0)y(j-1)+\\sum_{j=1}^nb_{ij}(1)y(j)+\\cdots+\\sum_{j=1}^nb_{ij}(N)y(j+N-1)=0 \\end{equation*} for $i=1,\\cdots, n$. The existence of solutions will be proved under a mild growth condition on the nonlinearity, $g$, which must hold only on a bounded subset of $\\{0,\\cdots, N\\}\\times\\mathbb{R}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06466","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"}