{"paper":{"title":"Positive solutions for nonlinear problems involving the one-dimensional {\\phi}-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Leandro Milne, Uriel Kaufmann","submitted_at":"2017-03-02T00:50:01Z","abstract_excerpt":"Let $\\Omega:=\\left( a,b\\right) \\subset\\mathbb{R}$, $m\\in L^{1}\\left( \\Omega\\right) $ and $\\lambda>0$ be a real parameter. Let $\\mathcal{L}$ be the differential operator given by $\\mathcal{L}u:=-\\phi\\left( u^{\\prime}\\right) ^{\\prime}+r\\left( x\\right) \\phi\\left( u\\right) $, where $\\phi :\\mathbb{R\\rightarrow R}$ is an odd increasing homeomorphism and $0\\leq r\\in L^{1}\\left( \\Omega\\right) $. We study the existence of positive solutions for problems of the form $\\mathcal{L}u=\\lambda m\\left( x\\right) f\\left( u\\right)$ in $\\Omega,$ $u=0$ on $\\partial\\Omega$, where $f:\\left[ 0,\\infty\\right) \\rightarro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00567","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"}