{"paper":{"title":"On the Structure of the Solution Set of a Sign Changing Perturbation of the p-Laplacian under Dirichlet Boundary Condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"J. V. Goncalves, M. R. Marcial","submitted_at":"2013-10-21T16:42:46Z","abstract_excerpt":"In a recent paper D. D. Hai showed that the equation $ -\\Delta_{p} u = \\lambda f(u) \\mbox{in} \\Omega$, under Dirichlet boundary condition, where $\\Omega \\subset {\\bf R^N}$ is a bounded domain with smooth boundary $\\partial\\Omega$, $\\Delta_{p}$ is the p-Laplacian, $f : (0,\\infty) \\rightarrow {\\bf R} $ is a continuous function which may blow up to $\\pm \\infty$ at the origin, admits a solution if $\\lambda > \\lambda_0$ and has no solution if $0 < \\lambda < \\lambda_0$. In this paper we show that the solution set $\\mathcal{S}$ of the equation above, which is not empty by Hai's results, actually admi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5636","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"}