{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NKHZMYL36ZZNQZV35574BL7RQR","short_pith_number":"pith:NKHZMYL3","schema_version":"1.0","canonical_sha256":"6a8f96617bf672d866bbef7fc0aff1845f3ecfb31952311ffc2ca60425a4740c","source":{"kind":"arxiv","id":"1711.10655","version":1},"attestation_state":"computed","paper":{"title":"Semi-classical Solutions For Fractional Schrodinger Equations With Potential Vanishing At Infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chaodong Xie, Shuangjie Peng, Xiaoming An","submitted_at":"2017-11-29T03:00:06Z","abstract_excerpt":"We study the following fractional Schr\\\"{o}dinger equation \\begin{equation}\\label{eq0.1} \\varepsilon^{2s}(-\\Delta)^s u + Vu = |u|^{p - 2}u,\\ \\ x\\in\\,\\,\\mathbb{R}^N. \\end{equation} We show that if the external potential $V\\in C(\\mathbb{R}^N;[0,\\infty))$ has a local minimum and $p\\in (2 + 2s/(N - 2s), 2^*_s)$, where $2^*_s=2N/(N-2s),\\,N\\ge 2s$, the problem has a family of solutions concentrating at the local minimum of $V$ provided that $\\liminf_{|x|\\to \\infty}V(x)|x|^{2s} > 0$. The proof is based on variational methods and penalized technique.\n  {\\textbf {Key words}: } fractional Schr\\\"{o}dinge"},"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":"1711.10655","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-29T03:00:06Z","cross_cats_sorted":[],"title_canon_sha256":"530900aa729d18ee13491c0dfe13ed84f3d176b87247c42231a3d79d77b86f30","abstract_canon_sha256":"eb89f58e5df94110740898d8b303e22e60dc1bff68a372bc0390474939f32e9c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:17.381662Z","signature_b64":"UdgAH3ooyGdDttc51CEZCrgK4s/5QKVXl7ZLDZrRZVvhuhy1HBRliXq/5pKs0soYF9PvVq4u0/xivfj/qv05CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a8f96617bf672d866bbef7fc0aff1845f3ecfb31952311ffc2ca60425a4740c","last_reissued_at":"2026-05-18T00:29:17.380939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:17.380939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semi-classical Solutions For Fractional Schrodinger Equations With Potential Vanishing At Infinity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chaodong Xie, Shuangjie Peng, Xiaoming An","submitted_at":"2017-11-29T03:00:06Z","abstract_excerpt":"We study the following fractional Schr\\\"{o}dinger equation \\begin{equation}\\label{eq0.1} \\varepsilon^{2s}(-\\Delta)^s u + Vu = |u|^{p - 2}u,\\ \\ x\\in\\,\\,\\mathbb{R}^N. \\end{equation} We show that if the external potential $V\\in C(\\mathbb{R}^N;[0,\\infty))$ has a local minimum and $p\\in (2 + 2s/(N - 2s), 2^*_s)$, where $2^*_s=2N/(N-2s),\\,N\\ge 2s$, the problem has a family of solutions concentrating at the local minimum of $V$ provided that $\\liminf_{|x|\\to \\infty}V(x)|x|^{2s} > 0$. The proof is based on variational methods and penalized technique.\n  {\\textbf {Key words}: } fractional Schr\\\"{o}dinge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10655","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1711.10655","created_at":"2026-05-18T00:29:17.381060+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.10655v1","created_at":"2026-05-18T00:29:17.381060+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.10655","created_at":"2026-05-18T00:29:17.381060+00:00"},{"alias_kind":"pith_short_12","alias_value":"NKHZMYL36ZZN","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"NKHZMYL36ZZNQZV3","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"NKHZMYL3","created_at":"2026-05-18T12:31:31.346846+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NKHZMYL36ZZNQZV35574BL7RQR","json":"https://pith.science/pith/NKHZMYL36ZZNQZV35574BL7RQR.json","graph_json":"https://pith.science/api/pith-number/NKHZMYL36ZZNQZV35574BL7RQR/graph.json","events_json":"https://pith.science/api/pith-number/NKHZMYL36ZZNQZV35574BL7RQR/events.json","paper":"https://pith.science/paper/NKHZMYL3"},"agent_actions":{"view_html":"https://pith.science/pith/NKHZMYL36ZZNQZV35574BL7RQR","download_json":"https://pith.science/pith/NKHZMYL36ZZNQZV35574BL7RQR.json","view_paper":"https://pith.science/paper/NKHZMYL3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.10655&json=true","fetch_graph":"https://pith.science/api/pith-number/NKHZMYL36ZZNQZV35574BL7RQR/graph.json","fetch_events":"https://pith.science/api/pith-number/NKHZMYL36ZZNQZV35574BL7RQR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NKHZMYL36ZZNQZV35574BL7RQR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NKHZMYL36ZZNQZV35574BL7RQR/action/storage_attestation","attest_author":"https://pith.science/pith/NKHZMYL36ZZNQZV35574BL7RQR/action/author_attestation","sign_citation":"https://pith.science/pith/NKHZMYL36ZZNQZV35574BL7RQR/action/citation_signature","submit_replication":"https://pith.science/pith/NKHZMYL36ZZNQZV35574BL7RQR/action/replication_record"}},"created_at":"2026-05-18T00:29:17.381060+00:00","updated_at":"2026-05-18T00:29:17.381060+00:00"}