{"paper":{"title":"On the indefinite Kirchhoff type problems with local sublinearity and linearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juntao Sun, Tsung-fang Wu","submitted_at":"2014-08-23T15:06:28Z","abstract_excerpt":"The purpose of this paper is to study the indefinite Kirchhoff type problem: \\begin{equation*} \\left\\{ \\begin{array}{ll} M\\left( \\int_{\\mathbb{R}^{N}}(|\\nabla u|^{2}+u^{2})dx\\right) \\left[ -\\Delta u+u\\right] =f(x,u) & \\text{in }\\mathbb{R}^{N}, \\\\ 0\\leq u\\in H^{1}\\left( \\mathbb{R}^{N}\\right), & \\end{array} \\right. \\end{equation*} where $N\\geq 1$, $M(t)=am\\left( t\\right) +b$, $m\\in C(\\mathbb{R}^{+})$ and $ f(x,u)=g(x,u)+h(x)u^{q-1}$. We require that $f$ is \\textquotedblleft local\\textquotedblright\\ sublinear at the origin and \\textquotedblleft local\\textquotedblright\\ linear at infinite. Using t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5502","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"}