In this article, we consider the existence of localized sign-changing solutions for the semiclassical Kirchhoff equation
where , is a small parameter, V(x) is a positive function that has a local minimum point P. When , 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
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