{"paper":{"title":"Limit profiles and uniqueness of ground states to the nonlinear Choquard equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jinmyoung Seok","submitted_at":"2017-04-01T06:50:55Z","abstract_excerpt":"Consider nonlinear Choquard equations \\begin{equation*} \\left\\{\\begin{array}{rcl} -\\Delta u +u & = &(I_\\alpha*|u|^p)|u|^{p-2}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 investigate limit profiles of ground states of nonlinear Choquard equations as $\\alpha \\to 0$ or $\\alpha \\to N$. This leads to the uniqueness and nondegeneracy of ground states when $\\alpha$ is sufficiently close to $0$ or close to $N$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00126","kind":"arxiv","version":3},"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"}