{"paper":{"title":"Some remarks on biharmonic elliptic problems with a singular nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Baishun Lai","submitted_at":"2011-01-20T13:52:52Z","abstract_excerpt":"We study the following semilinear biharmonic equation $$ \\left\\{\\begin{array}{lllllll} \\Delta^{2}u=\\frac{\\lambda}{1-u}, &\\quad \\mbox{in}\\quad \\B, u=\\frac{\\partial u}{\\partial n}=0, &\\quad \\mbox{on}\\quad \\partial\\B, \\end{array} \\right. %\\eqno(M_{\\lambda}) $$ where $\\B$ is the unit ball in $\\R^{n}$ and $n$ is the exterior unit normal vector. We prove the existence of $\\lambda^{*}>0$ such that for $\\lambda\\in (0,\\lambda^{*})$ there exists a minimal (classical) solution $\\underline{u}_{\\lambda}$, which satisfies $0<\\underline{u}_{\\lambda}<1$. In the extremal case $\\lambda=\\lambda^{*}$, we prove th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3904","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"}