{"paper":{"title":"Uniqueness of solutions for elliptic systems and fourth order equations involving a parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Craig Cowan","submitted_at":"2011-09-23T22:00:54Z","abstract_excerpt":"We examine the equation \\[\\Delta^2 u = \\lambda f(u) \\qquad \\Omega, \\] with either Navier or Dirichlet boundary conditions. We show some uniqueness results under certain constraints on the parameter $ \\lambda$. We obtain similar results for the sytem\n  {equation*} \\{{array}{rrl} -\\Delta u &=& \\lambda f(v) \\qquad \\Omega, -\\Delta v &=& \\gamma g(u) \\qquad \\Omega, u&=& v = 0 \\qquad \\partial Omega. {array}. {equation*}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5206","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"}