{"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 $q's$. We give also qualitative properties about the energy level of the solutions and a variational characterizat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05260","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"}