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The main tools are a local Pohozaev type of identity, blow-up analysis and the maximum principle. Our results also show that the asymptotic behavior of concentrated points to Schr\\\"odinger-Newton problem is quite different "},"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":"1703.00777","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-02T13:35:04Z","cross_cats_sorted":[],"title_canon_sha256":"a050f39b0409a6d0c64e2f9205f6bd0e6ea14976f2151d1a8e6dcd1758e271ff","abstract_canon_sha256":"200459addd10f0b863cf9659c4d59b7996efe1d7d0a2da5a79159dc7a5f845f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:40.786188Z","signature_b64":"28YqSS5XRmhlrb6NLQyUByqCO2UzXPDpxpAQfhabCXDqwbph7u9EJXt3aKEa02eoHUsOKohmT93qwtuuJNA3Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea860a80987c39713db1e7f6600a510cf14e72ce2aa532430b9c12870e1b5019","last_reissued_at":"2026-05-18T00:49:40.785693Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:40.785693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniqueness of positive solutions with Concentration for the Schr\\\"odinger-Newton problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chunhua Wang, Peng Luo, Shuangjie Peng","submitted_at":"2017-03-02T13:35:04Z","abstract_excerpt":"We are concerned with the following Schr\\\"odinger-Newton problem\n  \\begin{equation}\n  -\\varepsilon^2\\Delta u+V(x)u=\\frac{1}{8\\pi \\varepsilon^2}\n  \\big(\\int_{\\mathbb R^3}\\frac{u^2(\\xi)}{|x-\\xi|}d\\xi\\big)u,~x\\in \\mathbb R^3. \\end{equation} For $\\varepsilon$ small enough, we show the uniqueness of positive solutions concentrating at the nondegenerate critical points of $V(x)$. 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