{"paper":{"title":"Multiplicity and concentration behavior of solutions for a quasilinear problem involving $N$-functions via penalization method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ailton R. Silva, Claudianor O. Alves","submitted_at":"2015-06-17T13:39:33Z","abstract_excerpt":"In this work, we study the existence, multiplicity and concentration of positive solutions for the following class of quasilinear problem: \\[ - \\Delta_{\\Phi}u + V(\\epsilon x)\\phi(\\vert u\\vert)u = f(u)\\quad \\mbox{in} \\quad \\mathbb{R}^{N}, \\] where $\\Phi(t) = \\int_{0}^{\\vert t\\vert}\\phi(s)sds$ is a N-function, $ \\Delta_{\\Phi}$ is the $\\Phi$-Laplacian operator, $\\epsilon$ is a positive parameter, $ N\\geq 2$, $V : \\mathbb{R}^{N} \\rightarrow \\mathbb{R} $ is a continuous function and $f : \\mathbb{R} \\rightarrow \\mathbb{R} $ is a $C^{1}$-function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05331","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"}