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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1906.12013","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-28T02:00:49Z","cross_cats_sorted":[],"title_canon_sha256":"c541b8e36f35e50ee4545ae4eb04f5204301623ffcbbe281b8934f64a4f3086c","abstract_canon_sha256":"c7ba6c0723a67a56e2f25e51ec04100b11a8219df56c31780f8f4c5cef820f0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:59.528934Z","signature_b64":"Ppfl9l4VMu4WjS34KnWCgjex5H2pABtTTjJYpjE7x2Vm75JeXNu0kIuhCf4PxcQDaqQ/7N8c+V7UZKsmVa3TDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"639d0b84e1421056e6a2f091a976a39fd2b58a0d9d7964c231111ab1013945cb","last_reissued_at":"2026-05-17T23:41:59.528567Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:59.528567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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