Localized nodal solutions for semiclassical nonlinear Kirchhoff equations
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Date
2022-08-02
Authors
Wang, Lixia
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In 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.
Description
Keywords
Kirchhoff equations, Nodal solutions, Penalization method
Citation
Wang, L. (2022). Localized nodal solutions for semiclassical nonlinear Kirchhoff equations. <i>Electronic Journal of Differential Equations, 2022</i>(57), pp. 1-23.
Rights
Attribution 4.0 International