{"paper":{"title":"Multiplicity results for fractional magnetic problems involving exponential growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jo\\~ao Marcos do \\'O, Manass\\'es de Souza, Pawan Kumar Mishra","submitted_at":"2019-06-28T02:00:49Z","abstract_excerpt":"We study the following fractional elliptic equations of the type, \\begin{equation*} (-\\Delta)^{\\frac12}_A u = \\lambda u+f(|u|)u ,\\;\\textrm{in } \\;(-1, 1),\\; u=0\\;\\textrm{in } \\;\\mathbb R\\setminus (-1, 1), \\end{equation*} where $\\lambda$ is a positive real parameter and $(-\\Delta)^{\\frac12}_A$ is the fractional magnetic operator with $A:\\mathbb R\\to \\mathbb R$ being a smooth magnetic field. Using a classical critical point theorems, we prove the existence of multiple solutions in the non-resonant case when the nonlinear term $f(t)$ has a critical exponential growth in the sense of Trudinger-Mos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.12013","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"}