{"paper":{"title":"Constant sign Green's function for simply supported beam equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alberto Cabada, Lorena Saavedra","submitted_at":"2016-04-14T18:14:16Z","abstract_excerpt":"The aim of this paper consists on the study of the following fourth-order operator: \\begin{equation}\\label{Ec::T4} T[M]\\,u(t)\\equiv u^{(4)}(t)+p_1(t)\\,u\"'(t)+p_2(t)\\,u\"(t)+M\\,u(t)\\,,\\ t\\in I \\equiv [a,b]\\,, \\end{equation} coupled with the two point boundary conditions: \\begin{equation}\\label{Ec::cf} u(a)=u(b)=u\"(a)=u\"(b)=0\\,. \\end{equation}\n  So, we define the following space:\n  \\begin{equation}\\label{Ec::esp}\n  X=\\left\\lbrace u\\in C^4(I)\\quad\\mid\\quad u(a)=u(b)=u\"(a)=u\"(b)=0 \\right\\rbrace \\,.\n  \\end{equation}\n  Here $p_1\\in C^3(I)$ and $p_2\\in C^2(I)$.\n  By assuming that the second order line"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04245","kind":"arxiv","version":2},"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"}