{"paper":{"title":"Existence of least energy nodal solution with two nodal domains for a generalized Kirchhoff problem in an Orlicz Sobolev space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giovany M. Figueiredo, Jefferson A. Santos","submitted_at":"2015-11-16T14:59:18Z","abstract_excerpt":"We show the existence of a nodal solution with two nodal domains for a generalized Kirchhoff equation of the type $$ -M\\left(\\displaystyle\\int_\\Omega \\Phi(|\\nabla u|)dx\\right)\\Delta_\\Phi u = f(u) \\ \\ \\mbox{in} \\ \\ \\Omega, \\ \\ u=0 \\ \\ \\mbox{on} \\ \\ \\partial\\Omega, $$ where $\\Omega$ is a bounded domain in $\\mathbf{R}^N$, $M$ is a general $C^{1}$ class function, $f$ is a superlinear $C^{1}$ class function with subcritical growth, $\\Phi$ is defined for $t\\in \\mathbf{R}$ by setting $ \\Phi(t)=\\int_0^{|t|}\\phi(s)sds$, $\\Delta_\\Phi$ is the operator $\\Delta_\\Phi u:=div(\\phi(|\\nabla u|)\\nabla u)$. The p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04980","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"}