{"paper":{"title":"Liouville theorems for stable Lane-Emden systems and biharmonic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Craig Cowan","submitted_at":"2012-07-04T18:55:44Z","abstract_excerpt":"We examine the elliptic system given by {equation} \\label{system_abstract}\n  -\\Delta u = v^p, \\qquad -\\Delta v = u^\\theta, \\qquad \\{in} \\IR^N, {equation} for $ 1 < p \\le \\theta$ and the fourth order scalar equation {equation} \\label{fourth_abstract} \\Delta^2 u = u^\\theta, \\qquad \\{in $ \\IR^N$,} {equation} where $ 1 < \\theta$. We prove various Liouville type theorems for positive stable solutions. For instance we show there are no positive stable solutions of (\\ref{system_abstract}) (resp. (\\ref{fourth_abstract})) provided $ N \\le 10$ and $ 2 \\le p \\le \\theta$ (resp. $ N \\le 10$ and $1 < \\theta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1081","kind":"arxiv","version":3},"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"}