{"paper":{"title":"Existence and multiplicity of solutions for a class of quasilinear problems in Orlicz-Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudianor O. Alves, Karima Ait-Mahiout","submitted_at":"2016-04-04T10:52:32Z","abstract_excerpt":"This work is concerned with the existence and multiplicity of solutions for the following class of quasilinear problems $$ -\\Delta_{\\Phi}u+\\phi(|u|)u=f(u)~\\text{in} ~\\Omega_{\\lambda}, u(x)>0 ~\\text{in}~\\Omega_{\\lambda}, u=0~ \\mbox{on} ~\\partial\\Omega_{\\lambda}, $$ where $\\Phi(t)=\\int_0^{|t|} \\phi(s) s \\, ds $ is an $N-$function, $\\Delta_{\\Phi}$ is the $\\Phi-$Laplacian operator, \\linebreak $\\Omega_{\\lambda}=\\lambda \\Omega,$ $\\Omega$ is a smooth bounded domain in $\\mathbb{R}^N,$ $N \\geq 2$, $\\lambda$ is a positive parameter and $f: \\mathbb{R}\\rightarrow \\mathbb{R}$ is a continuous function. Here"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00808","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"}