{"paper":{"title":"Ground state solutions for a nonlinear Choquard equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luca Battaglia","submitted_at":"2017-01-09T22:23:20Z","abstract_excerpt":"We discuss the existence of ground state solutions for the Choquard equation $$-\\Delta u=(I_\\alpha*F(u))F'(u)\\quad\\quad\\quad\\text{in }\\mathbb R^N.$$ We prove the existence of solutions under general hypotheses, investigating in particular the case of a homogeneous nonlinearity $F(u)=\\frac{|u|^p}p$. The cases $N=2$ and $N\\ge3$ are treated differently in some steps. The solutions are found through a variational mountain pass strategy. The result presented are contained in the papers with arXiv ID 1212.2027 and 1604.03294"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02376","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"}