{"paper":{"title":"A characterization related to Schr\\\"odinger equations on Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Csaba Farkas, Francesca Faraci","submitted_at":"2017-04-07T08:35:57Z","abstract_excerpt":"In this paper we consider the following problem $$\\begin{cases} -\\Delta_{g}u+V(x)u=\\lambda\\alpha(x)f(u), & \\mbox{in }M\\\\ u\\geq0, & \\mbox{in }M\\\\ u\\to0, & \\mbox{as }d_{g}(x_{0},x)\\to\\infty \\end{cases}$$where $(M,g)$ is a $N$-dimensional ($N\\geq3)$, non-compact Riemannian manifold with asymptotically non-negative Ricci curvature, $\\lambda$ is a real parameter, $V$ is a positive coercive potential, $\\alpha$ is a bounded function and $f$ is a suitable nonlinearity. By using variational methods we prove a characterization result for existence of solutions for our problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02131","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"}