{"paper":{"title":"On the study of a class of non-linear differential equations on compact Riemannian Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Carlos Silva, Marcelo Souza, Romildo Pina","submitted_at":"2016-11-09T12:56:00Z","abstract_excerpt":"We study the existence of solutions of the non-linear differential equations on the compact Riemannian manifolds $(M^n,g), n\\geq 2$, \\Delta_p u + a(x)u^{p-1} = \\lambda f(u,x), (E2) where $\\Delta_p$ is the $p-$laplacian, with $1<p<n$. The equation (E2) generalizes a equation considered by Aubin, where he has considered, a compact Riemannian manifold $(M,g)$, the differential equation ($p=2$)  \\Delta u + a(x)u = \\lambda f(u,x), (E1) where $a(x)$ is a $C^{\\infty}$ function defined on $M$ and $f(u,x)$ is a $C^{\\infty}$ function defined on $\\mathbb{R}\\times M$. We show that the equation (E2) has so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02909","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"}