{"paper":{"title":"Blowing up Solutions for a Biharmonic Equation with Critical Nonlinearity","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Khalil El Mehdi, Mokhless Hammami","submitted_at":"2004-08-25T15:46:21Z","abstract_excerpt":"In this paper we consider the following biharmonic equation with critical exponent $P_\\epsilon$ : $\\Delta^2 u= Ku^{(n+4)/(n-4)-\\epsilon}, u>0$ in $\\Omega$ and $u=\\Delta u=0$ on $\\partial\\Omega$, where $\\Omega$ is a domain in $R^n$, $n\\geq 5$, $\\epsilon$ is a small positive parameter and $K$ is smooth positive function. We construct solutions of $P_\\epsilon$ which blow up and concentrate at strict local maximum of $K$ either at the boundary or in the interior of $\\Omega$. We also construct solutions of $P_\\epsilon$ concentrating at an interior strict local minimum of $K$. Finally, we prove a no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0408352","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"}