{"paper":{"title":"Multiple positive solutions of a Sturm-Liouville boundary value problem with conflicting nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Guglielmo Feltrin","submitted_at":"2016-07-28T09:00:02Z","abstract_excerpt":"We study the second order nonlinear differential equation \\begin{equation*} u\"+ \\sum_{i=1}^{m} \\alpha_{i} a_{i}(x)g_{i}(u) - \\sum_{j=0}^{m+1} \\beta_{j} b_{j}(x)k_{j}(u) = 0, \\end{equation*} where $\\alpha_{i},\\beta_{j}>0$, $a_{i}(x), b_{j}(x)$ are non-negative Lebesgue integrable functions defined in $\\mathopen{[}0,L\\mathclose{]}$, and the nonlinearities $g_{i}(s), k_{j}(s)$ are continuous, positive and satisfy suitable growth conditions, as to cover the classical superlinear equation $u\"+a(x)u^{p}=0$, with $p>1$. When the positive parameters $\\beta_{j}$ are sufficiently large, we prove the exi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08365","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"}