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We prove the existence of infinitely many solutions for the above problem by a finite dimensional reduction method combining various Pohazaev identies."},"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":"1904.08316","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-04-17T15:26:33Z","cross_cats_sorted":[],"title_canon_sha256":"203b10a15ccebe76c3b0badc469e6e6ec927d3499720c3ee9dbd35a490bea994","abstract_canon_sha256":"332ddce398702974d33e8069d8964bb6d81eda5167c791f06551f39201b5ed7c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:18.037955Z","signature_b64":"mPGaNq0OjQQHFRA/ZTIm0fh4ehnGseJdz4eZOA8yWqpLVgTfHhV1TZSL9S1ig463mzu2bf5CIv6nhQN3DkOzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ac030e2e71c9a74fd8347eec11e8bc4cf32325574547c1efc6dcfefcb13404b","last_reissued_at":"2026-05-17T23:48:18.037462Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:18.037462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solutions for fractional operator problem via local Pohozaev identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jianjun Nie, Ting Liu, Yuxia Guo","submitted_at":"2019-04-17T15:26:33Z","abstract_excerpt":"We consider the following fractional Schr\\\"{o}dinger equation involving critical exponent: \\begin{equation*} \\left\\{\\begin{array}{ll} (-\\Delta)^s u+V(|y'|,y'')u=u^{2^*_s-1} \\ \\hbox{ in } \\ \\mathbb{R}^N, \\\\ u>0, \\ y \\in \\mathbb{R}^N, \\end{array}\\right. \\end{equation*} where $s\\in(\\frac{1}{2}, 1)$, $(y',y'')\\in \\mathbb{R}^2\\times \\mathbb{R}^{N-2}$, $V(|y'|,y'')$ is a bounded nonnegative function with a weaker symmetry condition. 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