{"paper":{"title":"A Liouville theorem for a fourth order H\\'enon equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Craig Cowan","submitted_at":"2011-10-11T01:32:25Z","abstract_excerpt":"We examine the following fourth order H\\'enon equation\n\\label{pipe} \\Delta^2 u = |x|^\\alpha u^p \\qquad \\text{in}\\ \\IR^N,\nwhere $ 0 < \\alpha$. Define the Hardy-Sobolev exponent $ p_4(\\alpha):= \\frac{N+4 + 2 \\alpha}{N-4}$. We show that in dimension N=5 there are no positive bounded classical solutions of (\\ref{pipe}) provided $ 1 < p < p_4(\\alpha)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2246","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"}