{"paper":{"title":"Solutions for fourth-order Kirchhoff type elliptic equations involving concave-convex nonlinearities in $\\mathbb{R}^{N}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Dong-Lun Wu, Fengying Li","submitted_at":"2019-07-06T22:33:55Z","abstract_excerpt":"In this paper, we show the existence and multiplicity of solutions for the following fourth-order Kirchhoff type elliptic equations \\begin{eqnarray*} \\Delta^{2}u-M(\\|\\nabla u\\|_{2}^{2})\\Delta u+V(x)u=f(x,u),\\ \\ \\ \\ \\ x\\in \\mathbb{R}^{N}, \\end{eqnarray*} where $M(t):\\mathbb{R}\\rightarrow\\mathbb{R}$ is the Kirchhoff function, $f(x,u)=\\lambda k(x,u)+ h(x,u)$, $\\lambda\\geq0$, $k(x,u)$ is of sublinear growth and $h(x,u)$ satisfies some general 3-superlinear growth conditions at infinity. We show the existence of at least one solution for above equations for $\\lambda=0$. For $\\lambda>0$ small enough"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03200","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"}