{"paper":{"title":"On the solvability of third-order three point systems of differential equations with dependence on the first derivative","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Feliz Minh\\'os, Robert de Sousa","submitted_at":"2016-07-28T10:10:37Z","abstract_excerpt":"This paper presents sufficient conditions for the solvability of the third order three point boundary value problem \\begin{equation*} \\left\\{ \\begin{array}{c} -u^{\\prime \\prime \\prime }(t)=f(t,\\,v(t),\\,v^{\\prime }(t)) \\\\ -v^{\\prime \\prime \\prime }(t)=h(t,\\,u(t),\\,u^{\\prime }(t)) \\\\ u(0)=u^{\\prime }(0)=0,u^{\\prime }(1)=\\alpha u^{\\prime }(\\eta ) \\\\ v(0)=v^{\\prime }(0)=0,v^{\\prime }(1)=\\alpha v^{\\prime }(\\eta ).\n  \\end{array}\n  \\right. \\end{equation*} The arguments apply Green's function associated to the linear problem and the Guo--Krasnosel'ski\\u{\\i} theorem of compression-expansion cones. The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08390","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"}