{"paper":{"title":"Existence of nodal solutions for Dirac equations with singular nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Lo\\\"ic Le Treust (CEREMADE)","submitted_at":"2012-08-12T19:23:17Z","abstract_excerpt":"We prove, by a shooting method, the existence of infinitely many solutions of the form $\\psi(x^0,x) = e^{-i\\Omega x^0}\\chi(x)$ of the nonlinear Dirac equation {equation*} i\\underset{\\mu=0}{\\overset{3}{\\sum}} \\gamma^\\mu \\partial_\\mu \\psi- m\\psi - F(\\bar{\\psi}\\psi)\\psi = 0 {equation*} where $\\Omega>m>0,$ $\\chi$ is compactly supported and \\[F(x) = \\{{array}{ll} p|x|^{p-1} & \\text{if} |x|>0 0 & \\text{if} x=0 {array}.] with $p\\in(0,1),$ under some restrictions on the parameters $p$ and $\\Omega.$ We study also the behavior of the solutions as $p$ tends to zero to establish the link between these equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2453","kind":"arxiv","version":2},"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"}