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Under some asymptotic assumptions on $K(x)$ at infinity, we show that this problem has infinitely many non-radial positive solutions, whose energy can be made arbitrarily large."},"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":"1402.1902","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-09T01:07:17Z","cross_cats_sorted":[],"title_canon_sha256":"de687f268d4047f64fe6a2a9a25d19bbc0b6fa70e4c1830a9bd58bc1ab8db690","abstract_canon_sha256":"4e58d14f59148e2aeccaba24880c6b2176bfcca2cc11578e36a8770950f6f661"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:33.208821Z","signature_b64":"lH8oRBLP0tWN6Dkd6DlyDEwAcT7u+I6MPCP4RSqjqKkpX3xGws6ODLO8EbZ26F5kvUIVQiUoP0UoHuEKw8DoAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb1801a794c1248503e2fd14af9eb362ca4892b2ac625ef392cf672da74254a3","last_reissued_at":"2026-05-18T02:59:33.208145Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:33.208145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinitely many positive solutions for nonlinear fractional Schr\\\"{o}dinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jing Yang, Shuangjie Peng, Wei Long","submitted_at":"2014-02-09T01:07:17Z","abstract_excerpt":"We consider the following nonlinear fractional Schr\\\"{o}dinger equation $$ (-\\Delta)^su+u=K(|x|)u^p,\\ \\ u>0 \\ \\ \\hbox{in}\\ \\ R^N, $$ where $K(|x|)$ is a positive radial function, $N\\ge 2$, $0<s<1$, $1<p<\\frac{N+2s}{N-2s}$. 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