{"paper":{"title":"Constant sign solution for simply supported beam equation with non-homogeneous boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alberto Cabada, Lorena Saavedra","submitted_at":"2017-03-27T14:34:43Z","abstract_excerpt":"The aim of this paper is to study the following fourth-order operator:\n  T[p,c]\\,u(t)\\equiv u^{(4)}(t)-p\\,u\"(t)+c(t)\\,u(t)\\,,\\quad t\\in I\\equiv [a,b]\\,, coupled with the non-homogeneous simply supported beam boundary conditions: u(a)=u(b)=0\\,,\\quad u\"(a)=d_1\\leq0\\,,\\ u\"(b)=d_2\\leq 0\\,. \n  First, we prove a result which makes an equivalence between the strongly inverse positive (negative) character of this operator with the previously introduced boundary conditions and with the homogeneous boundary conditions, given by: \nT[p,c]\\,u(t)=h(t)(\\geq0)\\,, u(a)=u(b)=u\"(a)=u\"(b)=0\\,, \nOnce that we have "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09107","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"}