{"paper":{"title":"Schrodinger-Maxwell systems on compact Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Csaba Farkas","submitted_at":"2018-03-20T18:09:32Z","abstract_excerpt":"In this paper we are focusing to the following Schr\\\"odinger-Maxwell system $(\\mathcal{SM}_{\\Psi(\\lambda,\\cdot)}^{e})$:\n  \\[ \\begin{cases} -\\Delta_{g}u+\\beta(x)u+eu\\phi=\\Psi(\\lambda,x)f(u) & \\mathrm{in}\\ M -\\Delta_{g}\\phi+\\phi=qu^{2} & \\mathrm{\\mathrm{in}\\ M} \\end{cases} \\] where $(M,g)$ is a 3-dimensional compact Riemannian manifold without boundary, $e,q>0$ are positive numbers, $f:\\mathbb{R}\\to\\mathbb{R}$ is a continuous function, $\\beta\\in C^{\\infty}(M)$ and $\\Psi\\in C^{\\infty}(\\mathbb{R}_{+}\\times M)$ are positive functions. By various variational approaches, existence of multiple solutio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07579","kind":"arxiv","version":3},"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"}