{"paper":{"title":"On the study of solutions for a non linear differential equation on compact Riemannian Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Carlos R. Silva, Marcelo Souza","submitted_at":"2016-11-07T19:04:12Z","abstract_excerpt":"In this paper we study the existence of solutions for a class of non-linear differential equation on compact Riemannian manifolds. We establish a lower and upper solutions' method to show the existence of a smooth positive solution for the equation (EQ1) \\begin{equation}\n  \\label{E4} \\Delta u \\ + \\ a(x)u \\ = \\ f(x)F(u) \\ + \\ h(x)H(u), (EQ1) \\end{equation} where \\ $a, \\ f, \\ h$ \\ are positive smooth functions on $M^n$, a $n-$dimensional compact Riemannian manifold, and \\ $ F, \\ H$ \\ are non-decreasing smooth functions on $\\mathbb{R}$. In \\cite{djadli} the equation (EQ1) was studied when $F(u)=u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02214","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"}