{"paper":{"title":"Existence and profile of ground-state solutions to a $1-$Laplacian problem in $\\mathbb{R}^N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudianor O. Alves, Giovany M. Figueiredo, Marcos T. O. Pimenta","submitted_at":"2018-04-18T20:06:59Z","abstract_excerpt":"In this work we prove the existence of ground state solutions for the following class of problems \\begin{equation*} \\left\\{ \\begin{array}{ll} \\displaystyle - \\Delta_1 u + (1 + \\lambda V(x))\\frac{u}{|u|} & = f(u), \\quad x \\in \\mathbb{R}^N, \\\\ u \\in BV(\\mathbb{R}^N), & \\end{array} \\right. \\label{Pintro} \\end{equation*} \\end{abstract} where $\\lambda > 0$, $\\Delta_1$ denotes the $1-$Laplacian operator which is formally defined by $\\Delta_1 u = \\mbox{div}(\\nabla u/|\\nabla u|)$, $V:\\mathbb{R}^N \\to \\mathbb{R}$ is a potential satisfying some conditions and $f:\\mathbb{R} \\to \\mathbb{R}$ is a subcritic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07618","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"}