{"paper":{"title":"Three positive solutions to an indefinite Neumann problem: a shooting method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Elisa Sovrano, Guglielmo Feltrin","submitted_at":"2017-06-09T10:00:02Z","abstract_excerpt":"We deal with the Neumann boundary value problem \\begin{equation*} \\begin{cases} \\, u\" + \\bigl{(} \\lambda a^{+}(t)-\\mu a^{-}(t) \\bigr{)}g(u) = 0, \\\\ \\, 0 < u(t) < 1, \\quad \\forall\\, t\\in\\mathopen{[}0,T\\mathclose{]},\\\\ \\, u'(0) = u'(T) = 0, \\end{cases} \\end{equation*} where the weight term has two positive humps separated by a negative one and $g\\colon \\mathopen{[}0,1\\mathclose{]} \\to \\mathbb{R}$ is a continuous function such that $g(0)=g(1)=0$, $g(s) > 0$ for $0<s<1$ and $\\lim_{s\\to0^{+}}g(s)/s=0$. We prove the existence of three solutions when $\\lambda$ and $\\mu$ are positive and sufficiently "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02880","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"}