{"paper":{"title":"Nonlinear Schr\\\"odinger equation in the Bopp-Podolsky electrodynamics: solutions in the electrostatic case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gaetano Siciliano, Pietro d'Avenia","submitted_at":"2018-02-09T18:42:47Z","abstract_excerpt":"We study the following nonlinear Schr\\\"odinger-Bopp-Podolsky system \\[ \\begin{cases} -\\Delta u + \\omega u + q^{2}\\phi u = |u|^{p-2}u -\\Delta \\phi + a^2 \\Delta^2 \\phi = 4\\pi u^2 \\end{cases} \\hbox{ in }\\mathbb{R}^3 \\] with $a,\\omega>0$. We prove existence and nonexistence results depending on the parameters $q,p$. Moreover we also show that, in the radial case, the solutions we find tend to solutions of the classical Schr\\\"odinger-Poisson system as $a\\to0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03380","kind":"arxiv","version":3},"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"}