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In the mass-critical case $\\alpha=\\frac{4}{d}$, we prove the global existence and blowup below ground states for the equation with $d\\geq 3$ and $c>-\\lambda(d)$. In the mass and energy intercritical case $\\frac{4}{d}<\\alpha<\\frac{4}{d-2}"},"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":"1711.04792","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-13T19:02:12Z","cross_cats_sorted":[],"title_canon_sha256":"b0b7d4b727146feeafdfecbb37dbbde7654216e0e016b5c68212e012b6dc0907","abstract_canon_sha256":"b65a599d531e3e7ae28ce924859e96bfdff3bc39886e32e3a1ffa7a3db3ae891"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:31.300660Z","signature_b64":"3P4bc8KkTJNZjdrcu+Tj+qVm2bvQHJ1mORxKEv9AU/nymTniwWuRlC+l+c9eC5OlR8FCkTQNIeaCavrpg01ODQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"deef2b520e663204cf19718dac23c00bf177576d9ab1c87f6de3e1a3a9545be1","last_reissued_at":"2026-05-18T00:08:31.300177Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:31.300177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global existence and blowup for a class of the focusing nonlinear Schr\\\"odinger equation with inverse-square potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Van Duong Dinh","submitted_at":"2017-11-13T19:02:12Z","abstract_excerpt":"We consider a class of the focusing nonlinear Schr\\\"odinger equation with inverse-square potential \\[ i\\partial_t u + \\Delta u -c|x|^{-2}u = - |u|^\\alpha u, \\quad u(0)=u_0 \\in H^1, \\quad (t,x)\\in \\mathbb{R} \\times \\mathbb{R}^d, \\] where $d\\geq 3$, $\\frac{4}{d}\\leq \\alpha \\leq \\frac{4}{d-2}$ and $c\\ne 0$ satisfies $c>-\\lambda(d):=-\\left(\\frac{d-2}{2}\\right)^2$. In the mass-critical case $\\alpha=\\frac{4}{d}$, we prove the global existence and blowup below ground states for the equation with $d\\geq 3$ and $c>-\\lambda(d)$. 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