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. Electronic Journal of Differential Equations, 2022(57), pp. 1-23.
Rights
Attribution 4.0 International