Fan, Haining2023-05-252023-05-252016-01-04Fan, H. (2016). Existence and concentration of ground state solutions for a Kirchhoff type problem. <i>Electronic Journal of Differential Equations, 2016</i>(05), pp. 1-18.1072-6691https://hdl.handle.net/10877/16877This article concerns the Kirchhoff type problem -(ε2α + εb ∫ℝ3|∇u|2dx)∆u + V(x)u = K(x)|u|p-1u, x ∈ ℝ3, u ∈ H1(ℝ3), where α, b are positive constants, 2 < p < 5, ε > 0 is a small parameter, and V(x), K(x) ∈ C1(ℝ3). Under certain assumptions on the non-constant potentials V(x) and K(x), we prove the existence and concentration properties of a positive ground state solution as ε → 0. Our main tool is a Nehari-Pohozaev manifold.Text18 pages1 file (.pdf)enAttribution 4.0 InternationalNehari-Pohozaev manifoldNonlocal problemPositive solutionConcentration propertyArticle