{"paper":{"title":"Nonlinear Choquard equations: doubly critical case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jinmyoung Seok","submitted_at":"2017-07-25T06:02:46Z","abstract_excerpt":"Consider nonlinear Choquard equations \\begin{equation*} \\left\\{\\begin{array}{rcl} -\\Delta u +u & = &(I_\\alpha*F(u))F'(u) \\quad \\text{in } \\mathbb{R}^N, \\\\ \\lim_{x \\to \\infty}u(x) & = &0, \\end{array}\\right. \\end{equation*} where $I_\\alpha$ denotes Riesz potential and $\\alpha \\in (0, N)$. In this paper, we show that when $F$ is doubly critical, i.e. $F(u) = \\frac{N}{N+\\alpha}|u|^{\\frac{N+\\alpha}{N}}+\\frac{N-2}{N+\\alpha}|u|^{\\frac{N+\\alpha}{N-2}}$, the nonlinear Choquard equation admits a nontrivial solution if $N \\geq 5$ and $\\alpha + 4 < N$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07820","kind":"arxiv","version":1},"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"}