Localized nodal solutions for semiclassical nonlinear Kirchhoff equations

Date

2022-08-02

Authors

Wang, Lixia

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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

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