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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 $N$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1704.00126","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-01T06:50:55Z","cross_cats_sorted":[],"title_canon_sha256":"9fba77d2acdd2d2ea12f935dedc17745c283023c6bf5783f2bbf15ceec13a601","abstract_canon_sha256":"dfc0c56abee95a0d7090c5bf11d80b7801916997c495bd7c23ae87e978096687"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:22.600818Z","signature_b64":"z6kKpH7jg1L3uKkQTv1njNPaByd4AVa/aRSGjRUnVuWDj1oEY32e87vsBXSMt5RwMq4DQyJmap35MqlMYk8cBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01d5b92b1062d479a0b1f361f65960941c5750df64441a06bcae00058104946b","last_reissued_at":"2026-05-18T00:24:22.600406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:22.600406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\alpha \\to N$. 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