{"paper":{"title":"Asymptotic behavior of a fourth order mean field equation with Dirichlet boundary condition","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Frederic Robert, Juncheng Wei","submitted_at":"2007-06-05T09:45:41Z","abstract_excerpt":"We consider asymptotic behavior of the following fourth order equation \\[ \\Delta^2 u= \\rho \\frac{e^{u}}{\\int_\\Om e^{u} dx} {in} \\Om, u= \\partial_\\nu u=0 {on} \\partial \\Omega \\] where $\\Om$ is a smooth oriented bounded domain in $\\R^4$. Assuming that $0<\\rho \\leq C$, we completely characterize the asymptotic behavior of the unbounded solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.0615","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"}