{"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. We show that symmetric groun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01519","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"}