{"paper":{"title":"Non-spurious solutions to discrete boundary value problems through variational methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ewa Schmeidel, Marek Galewski","submitted_at":"2015-03-05T22:25:33Z","abstract_excerpt":"Using direct variational method we consider the existence of non-spurious solutions to the following Dirichlet problem $\\ddot{x}\\left( t\\right) =f\\left( t,x\\left( t\\right) \\right) $, $x\\left( 0\\right) =x\\left( 1\\right) =0 $ where $f:\\left[ 0,1\\right] \\times \\mathbb{R} \\rightarrow \\mathbb{R}$ is a jointly continuous function convex in $x$ which does not need to satisfy any further growth conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01807","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"}