{"paper":{"title":"On the fractional Schr\\\"{o}dinger-Kirchhoff equations with electromagnetic fields and critical nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Binlin Zhang, Du\\v{s}an Repov\\v{s}, Sihua Liang","submitted_at":"2018-03-15T11:20:37Z","abstract_excerpt":"We consider the fractional Schr\\\"{o}dinger-Kirchhoff equations with electromagnetic fields and critical nonlinearity $\\varepsilon^{2s}M([u]_{s,A_\\varepsilon}^2)(-\\Delta)_{A_\\varepsilon}^su + V(x)u =$ $|u|^{2_s^\\ast-2}u + h(x,|u|^2)u,$ $\\ \\ x\\in \\mathbb{R}^N,$ where $ u(x) \\rightarrow 0$ as $|x| \\rightarrow \\infty,$ and $(-\\Delta)_{A_\\varepsilon}^s$ is the fractional magnetic operator with $0<s<1$, $2_s^\\ast = 2N/(N-2s),$ $M : \\mathbb{R}^{+}_{0} \\rightarrow \\mathbb{R}^{+}$ is a continuous nondecreasing function, $V:\\mathbb{R}^N \\rightarrow \\mathbb{R}^+_0,$ and $A: \\mathbb{R}^N \\rightarrow \\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05694","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"}