{"paper":{"title":"Nodal solutions for the 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","submitted_at":"2015-03-20T10:06:36Z","abstract_excerpt":"We consider the general Choquard equations $$\n  -\\Delta u + u = (I_\\alpha \\ast |u|^p) |u|^{p - 2} u $$ where $I_\\alpha$ is a Riesz potential. We construct minimal action odd solutions for $p \\in (\\frac{N + \\alpha}{N}, \\frac{N + \\alpha}{N - 2})$ and minimal action nodal solutions for $p \\in (2,\\frac{N + \\alpha}{N - 2})$. We introduce a new minimax principle for least action nodal solutions and we develop new concentration-compactness lemmas for sign-changing Palais--Smale sequences. The nonlinear Schr\\\"odinger equation, which is the nonlocal counterpart of the Choquard equation, does not have s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06031","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"}