{"paper":{"title":"Existence of groundstates for a class of nonlinear Choquard equations in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jean Van Schaftingen, Luca Battaglia","submitted_at":"2016-04-12T08:26:34Z","abstract_excerpt":"We prove the existence of a nontrivial groundstate solution for the class of nonlinear Choquard equation $$ -\\Delta u+u=(I_\\alpha*F(u))F'(u)\\qquad\\text{in }\\mathbb{R}^2, $$ where $I_\\alpha$ is the Riesz potential of order $\\alpha$ on the plane $\\mathbb{R}^2$ under general nontriviality, growth and subcriticality on the nonlinearity $F \\in C^1 (\\mathbb{R},\\mathbb{R})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03294","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"}