{"paper":{"title":"Nonlocal Schr\\\"odinger-Kirchhoff equations with external magnetic field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Binlin Zhang, Marco Squassina, Patrizia Pucci, Xiang Mingqi","submitted_at":"2016-05-18T18:26:45Z","abstract_excerpt":"The paper deals with existence and multiplicity of solutions of the fractional Schr\\\"{o}dinger--Kirchhoff equation involving an external magnetic potential. As a consequence, the results can be applied to the special case \\begin{equation*} (a+b[u]_{s,A}^{2\\theta-2})(-\\Delta)_A^su+V(x)u=f(x,|u|)u\\,\\, \\quad \\text{in $\\mathbb{R}^N$}, \\end{equation*} where $s\\in (0,1)$, $N>2s$, $a\\in \\mathbb{R}^+_0$, $b\\in \\mathbb{R}^+_0$, $\\theta\\in[1,N/(N-2s))$, $A:\\mathbb{R}^N\\rightarrow\\mathbb{R}^N$ is a magnetic potential, $V:\\mathbb{R}^N\\rightarrow \\mathbb{R}^+$ is an electric potential, $(-\\Delta )_A^s$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05689","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"}