{"paper":{"title":"Multiplicity and concentration results for a fractional Schr\\\"odinger-Poisson type equation with magnetic field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Vincenzo Ambrosio","submitted_at":"2018-07-18T11:04:15Z","abstract_excerpt":"This paper is devoted to the study of fractional Schr\\\"odinger-Poisson type equations with magnetic field of the type \\begin{equation*} \\varepsilon^{2s}(-\\Delta)_{A/\\varepsilon}^{s}u+V(x)u+\\varepsilon^{-2t}(|x|^{2t-3}*|u|^{2})u=f(|u|^{2})u \\quad \\mbox{ in } \\mathbb{R}^{3}, \\end{equation*} where $\\varepsilon>0$ is a parameter, $s,t\\in (0, 1)$ are such that $2s+2t>3$, $A:\\mathbb{R}^{3}\\rightarrow \\mathbb{R}^{3}$ is a smooth magnetic potential, $(-\\Delta)^{s}_{A}$ is the fractional magnetic Laplacian, $V:\\mathbb{R}^{3}\\rightarrow \\mathbb{R}$ is a continuous electric potential and $f:\\mathbb{R}\\ri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06861","kind":"arxiv","version":2},"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"}