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We show that symmetric groun"},"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":"1501.01519","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-07T15:25:20Z","cross_cats_sorted":[],"title_canon_sha256":"4fd521191082295e716ec09ec2d5e0db0404a27857cfb10b68808b294b75fe45","abstract_canon_sha256":"6a0b923fb429c6323da7e55f23275282487eee55b3d3af8081f36947aee44c8b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:51.050733Z","signature_b64":"lt3pYHGvkTj0/VtFgdN2FR4YRO9hJOXZ8SHKEPKUSt5GcbUMplmVRGM9OEf/jUFQt75PDv4MZTn+362JQlPxBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9c5791affba09589f943ab3889c764571c73fbeba887437056ba5fe0d6c72fd","last_reissued_at":"2026-05-18T01:09:51.050097Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:51.050097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ground states of critical and supercritical problems of Brezis-Nirenberg type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrzej Szulkin, Angela Pistoia, M\\'onica Clapp","submitted_at":"2015-01-07T15:25:20Z","abstract_excerpt":"We study the existence of symmetric ground states to the supercritical problem \\[ -\\Delta v=\\lambda v+\\left\\vert v\\right\\vert ^{p-2}v\\text{ \\ in }\\Omega,\\qquad v=0\\text{ on }\\partial\\Omega, \\] in a domain of the form \\[ \\Omega=\\{(y,z)\\in\\mathbb{R}^{k+1}\\times\\mathbb{R}^{N-k-1}:\\left( \\left\\vert y\\right\\vert ,z\\right) \\in\\Theta\\}, \\] where $\\Theta$ is a bounded smooth domain such that $\\overline{\\Theta} \\subset\\left( 0,\\infty\\right) \\times\\mathbb{R}^{N-k-1},$ $1\\leq k\\leq N-3,$ $\\lambda\\in\\mathbb{R},$ and $p=\\frac{2(N-k)}{N-k-2}$ is the $(k+1)$-st critical exponent. 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