{"paper":{"title":"Nonlinear fractional magnetic Schr\\\"odinger equation: existence and multiplicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pietro d'Avenia, Vincenzo Ambrosio","submitted_at":"2017-09-24T15:15:07Z","abstract_excerpt":"In this paper we focus our attention on the following nonlinear fractional Schr\\\"odinger equation with magnetic field \\begin{equation*} \\varepsilon^{2s}(-\\Delta)_{A/\\varepsilon}^{s}u+V(x)u=f(|u|^{2})u \\quad \\mbox{ in } \\mathbb{R}^{N}, \\end{equation*} where $\\varepsilon>0$ is a parameter, $s\\in (0, 1)$, $N\\geq 3$, $(-\\Delta)^{s}_{A}$ is the fractional magnetic Laplacian, $V:\\mathbb{R}^{N}\\rightarrow \\mathbb{R}$ and $A:\\mathbb{R}^{N}\\rightarrow \\mathbb{R}^N$ are continuous potentials and $f:\\mathbb{R}^{N}\\rightarrow \\mathbb{R}$ is a subcritical nonlinearity. By applying variational methods and L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08207","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"}