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We prove, by means of the fibering approach, that the system has no solutions at all for large values of $q's$, and has two radial solutions for small $q's$. We give also qualitative properties about the energy level of the solutions and a variational characterizat"},"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":"1806.05260","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-13T20:39:38Z","cross_cats_sorted":[],"title_canon_sha256":"c4a5f233beeeece0fec1160385ffc7a9eed7c1a620a8d7ea6e60491ff3fd9e31","abstract_canon_sha256":"e590be29923b3c32e015550ddd0a8ed6895508c8faca42d7614ee622d2a61467"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:16.608426Z","signature_b64":"sV20Vj+QG+81VTmZtakgfPZDn+Irx2hUnOm6+HAf8d4wdezgA9guxdvrY+Eh8gp/uLfmXwn3uygBr5kTMTsfAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c12edea01a8897784991d9b06c99ef7e744ed3a15437ad2426b8f38a68eff059","last_reissued_at":"2026-05-18T00:13:16.607733Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:16.607733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The fibering method approach for a non-linear Schr\\\"odinger equation coupled with the electromagnetic field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gaetano Siciliano, Kaye Silva","submitted_at":"2018-06-13T20:39:38Z","abstract_excerpt":"We study, with respect to the parameter $q\\neq0$, the following Schr\\\"odinger-Bopp-Podolsky system in $\\mathbb R^{3}$ \\begin{equation*} \\left\\{ \\begin{aligned} -&\\Delta u+\\omega u+q^2\\phi u=|u|^{p-2}u, \\\\ &-\\Delta \\phi+a^2\\Delta^2 \\phi = 4\\pi u^2, \\end{aligned} \\right.\n  \\end{equation*} where $p\\in(2,3], \\omega>0, a\\geq0$ are fixed. We prove, by means of the fibering approach, that the system has no solutions at all for large values of $q's$, and has two radial solutions for small $q's$. 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