{"paper":{"title":"Existence of solution for a class of quasilinear problem in Orlicz-Sobolev space without $\\Delta_2$-condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudianor O. Alves, Edcarlos D. Silva, Marcos T. O. Pimenta","submitted_at":"2017-04-11T22:52:02Z","abstract_excerpt":"\\noindent In this paper we study existence of solution for a class of problem of the type $$ \\left\\{ \\begin{array}{ll} -\\Delta_{\\Phi}{u}=f(u), \\quad \\mbox{in} \\quad \\Omega u=0, \\quad \\mbox{on} \\quad \\partial \\Omega, \\end{array} \\right. $$ where $\\Omega \\subset \\mathbb{R}^N$, $N \\geq 2$, is a smooth bounded domain, $f:\\mathbb{R} \\to \\mathbb{R}$ is a continuous function verifying some conditions, and $\\Phi:\\mathbb{R} \\to \\mathbb{R}$ is a N-function which is not assumed to satisfy the well known $\\Delta_2$-condition, then the Orlicz-Sobolev space $W^{1,\\Phi}_0(\\Omega)$ can be non reflexive. As ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03562","kind":"arxiv","version":2},"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"}