Qian, XiaotaoChen, Jianqing2022-02-162022-02-162018-07-17Qian, X., & Chen, J. (2018). Existence of multiple solutions and estimates of extremal values for a Kirchhoff type problem with fast increasing weight and critical nonlinearity. <i>Electronic Journal of Differential Equations, 2018</i>(144), pp. 1-19.1072-6691https://hdl.handle.net/10877/15344In this article, we study the Kirchhoff type problem -(α + ε ∫ℝ3 K(x)|∇u|2dx) div(K(x)∇u) = λK(x)ƒ(x)|u|q-2u + K(x)|u|4u, where x ∈ ℝ3, 1 < q < 2, K(x) = exp(|x|α/4) with α ≥ 2, ε > 0 is small enough, and the parameters α, λ > 0. Under some assumptions on ƒ(x), we establish the existence of two nonnegative nontrivial solutions and obtain uniform lower estimates for extremal values of the problem via variational methods.Text19 pages1 file (.pdf)enAttribution 4.0 InternationalVariational methodsKirchhoff type equationCritical nonlinearityMultiple solutionsExtremal valuesArticle