{"paper":{"title":"Elliptic problems on complete non-compact Riemannian manifolds with asymptotically non-negative Ricci curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giovanni Molica Bisci, Simone Secchi","submitted_at":"2018-03-20T15:44:55Z","abstract_excerpt":"In this paper we discuss the existence and non--existence of weak solutions to parametric equations involving the Laplace-Beltrami operator $\\Delta_g$ in a complete non-compact $d$--dimensional ($d\\geq 3$) Riemannian manifold $(\\mathcal{M},g)$ with asymptotically non--negative Ricci curvature and intrinsic metric $d_g$. Namely, our simple model is the following problem $$ \\left\\{ \\begin{array}{ll} -\\Delta_gw+V(\\sigma)w=\\lambda \\alpha(\\sigma)f(w) & \\mbox{ in } \\mathcal{M}\\\\ w\\geq 0 & \\mbox{ in } \\mathcal{M} \\end{array}\\right. $$ where $V$ is a positive coercive potential, $\\alpha$ is a positive"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07494","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"}