{"paper":{"title":"A note on the implicit function theorem for quasi-linear eigenvalue problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Robin Nittka","submitted_at":"2011-09-23T14:27:00Z","abstract_excerpt":"We consider the quasi-linear eigenvalue problem $-\\Delta_p u = \\lambda g(u)$ subject to Dirichlet boundary conditions on a bounded open set $\\Omega$, where $g$ is a locally Lipschitz continuous functions. Imposing no further conditions on $\\Omega$ or $g$ we show that for small $\\lambda$ the problem has a bounded solution which is unique in the class of all small solutions. Moreover, this curve of solutions depends continuously on $\\lambda$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5089","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"}