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Recently, for nonlinear Schr\\\"odinger equations with a harmonic potential, Ohta (2018) proved that if $\\partial_\\lambda^2S_\\omega(\\phi_\\omega^\\lambda)|_{\\lambda=1}\\le0$, then the standing wave is strongly unstable, where $S_\\omega$ is the action, and $\\"},"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":"1804.02127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-06T04:21:02Z","cross_cats_sorted":[],"title_canon_sha256":"2c33398b4cd41cb4d1e5942f93db2270e166084ccd9b8be3dbf51ddb5992f7f2","abstract_canon_sha256":"d571ccc50a27ce572031197992442ceb6ac2a0ee9e4982af4a3e55224210a9f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:05.742464Z","signature_b64":"5+h/+P4RfwdStpAUYIFPVqurPqIcLWYWdRvPJaP9GfOOAKIxVglbXtSNEEx5O9BR8hAv8Pul6mXMWhxBkLtrAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3ea8b7b42b3e9eb6d7ef306dfb66940e286336ae6fc29b2c84673f95c77d6b2","last_reissued_at":"2026-05-18T00:19:05.741852Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:05.741852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong instability of standing waves for nonlinear Schr\\\"odinger equations with attractive inverse power potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masahito Ohta, Noriyoshi Fukaya","submitted_at":"2018-04-06T04:21:02Z","abstract_excerpt":"We study the strong instability of standing waves $e^{i\\omega t}\\phi_\\omega(x)$ for nonlinear Schr\\\"{o}dinger equations with an $L^2$-supercritical nonlinearity and an attractive inverse power potential, where $\\omega\\in\\mathbb{R}$ is a frequency, and $\\phi_\\omega\\in H^1(\\mathbb{R}^N)$ is a ground state of the corresponding stationary equation. 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