Wang, Lixia2023-04-252023-04-252022-08-02Wang, L. (2022). Localized nodal solutions for semiclassical nonlinear Kirchhoff equations. <i>Electronic Journal of Differential Equations, 2022</i>(57), pp. 1-23.1072-6691https://hdl.handle.net/10877/16647In this article, we consider the existence of localized sign-changing solutions for the semiclassical Kirchhoff equation -(ε2α + εb ∫ℝ3 |∇u|2dx)∆u + V(x)u = |u|p-2u, x ∈ ℝ3, u ∈ H1(ℝ3) where 4 < p < 2* = 6, ε > 0 is a small parameter, V(x) is a positive function that has a local minimum point P. When ε → 0, by using a minimax characterization of higher dimensional symmetric linking structure via the symmetric mountain pass theorem, we obtain an infinite sequence of localized sign-changing solutions clustered at the point P.Text23 pages1 file (.pdf)enAttribution 4.0 InternationalKirchhoff equationsNodal solutionsPenalization methodArticle