{"paper":{"title":"Least action nodal solutions for the quadratic Choquard equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jean Van Schaftingen, Marco Ghimenti, Vitaly Moroz","submitted_at":"2015-11-15T23:15:57Z","abstract_excerpt":"We prove the existence of a minimal action nodal solution for the quadratic Choquard equation $$ -\\Delta u + u = \\big(I_\\alpha \\ast |u|^2\\big)u \\quad\\text{in }\\; \\mathbb R^N,$$ where $I_\\alpha$ is the Riesz potential of order $\\alpha\\in(0,N)$. The solution is constructed as the limit of minimal action nodal solutions for the nonlinear Choquard equations $$\n  -\\Delta u + u = \\big(I_\\alpha \\ast |u|^p\\big)|u|^{p-2}u \\quad\\text{in }\\; \\mathbb R^N$$ when $p\\searrow 2$. The existence of minimal action nodal solutions for $p>2$ can be proved using a variational minimax procedure over Nehari nodal set"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04779","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"}