Electron. J. Differential Equations, Vol. 2022 (2022), No. 57, pp. 1-23.

Localized nodal solutions for semiclassical nonlinear Kirchhoff equations

Lixia Wang

In this article, we consider the existence of localized sign-changing solutions for the semiclassical Kirchhoff equation

where $4<p<2^{\ast}=6$ , $\varepsilon>0$ is a small parameter, V(x) is a positive function that has a local minimum point P. When $\varepsilon\to 0$ , 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.

Submitted April 18, 2022. Published August 2, 2022.
Math Subject Classifications: 35J20, 35J60.
Key Words: Kirchhoff equations; nodal solutions; penalization method.

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Lixia Wang
School of Sciences
Tianjin Chengjian University
Tianjin 300384, China
email: wanglixia0311@126.com

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