{"paper":{"title":"Existence of solutions for a higher order Kirchhoff type problem with exponential critical growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Liang Zhao, Ning Zhang","submitted_at":"2015-07-19T12:33:44Z","abstract_excerpt":"The higher order Kirchhoff type equation $$\\int_{\\mathbb{R}^{2m}}(|\\nabla^m u|^2 +\\sum_{\\gamma=0}^{m-1}a_{\\gamma}(x)|\\nabla^{\\gamma}u|^2)dx \\left((-\\Delta)^m u+\\sum_{\\gamma=0}^{m-1}(-1)^\\gamma \\nabla^\\gamma\\cdot(a_\\gamma (x)\\nabla^\\gamma u)\\right) =\\frac{f(x,u)}{|x|^\\beta}+\\epsilon h(x)\\ \\ \\text{in}\\ \\ \\mathbb{R}^{2m}$$ is considered in this paper. We assume that the nonlinearity of the equation has exponential critical growth and prove that, for a positive $\\epsilon$ which is small enough, there are two distinct nontrivial solutions to the equation. When $\\epsilon=0$, we also prove that the e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05280","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"}