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Our results are in clear accordance with those for the classical local counterpart, that is when $s=1$."},"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":"1202.0576","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-02-02T22:24:34Z","cross_cats_sorted":[],"title_canon_sha256":"9c9acf0ceb2cd79e9765670c82e77871eb16a79d751a12359379a3f62006604e","abstract_canon_sha256":"fda67c654ca7edadf113b4b6e3f62af6c15c18c234c23db237751760ff26c335"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:23.938364Z","signature_b64":"B5uKpgOq/+WeUPHmATNqPOPiK6GWXHxJHeCYShhiCCEr32vYwwveU/m65DRSzGDiXnuZE+UIMbc+NswgXK93AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6259b4b9b1d7fe0ea1679f03e7695f581893d9f46eb3401929eca5266ce9c408","last_reissued_at":"2026-05-18T03:42:23.937838Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:23.937838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence and symmetry results for a Schr\\\"odinger type problem involving the fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enrico Valdinoci, Giampiero Palatucci, Serena Dipierro","submitted_at":"2012-02-02T22:24:34Z","abstract_excerpt":"This paper deals with the following class of nonlocal Schr\\\"odinger equations $$ \\displaystyle (-\\Delta)^s u + u = |u|^{p-1}u \\ \\ \\text{in} \\ \\mathbb{R}^N, \\quad \\text{for} \\ s\\in (0,1). $$ We prove existence and symmetry results for the solutions $u$ in the fractional Sobolev space $H^s(\\mathbb{R}^N)$. 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