Yongpeng Chen, Zhipeng Yang, Existence of multi-bump solutions for a nonlinear Kirchhoff equation

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DOI: 10.23952/jnva.8.2024.2.03

Volume 8, Issue 2, 1 April 2024, Pages 233-248

Abstract. We consider the following Kirchhoff problem

$-\left(a+b \int_{\mathbb{R}^3}|\nabla u|^2 \right) \Delta u+(1+\varepsilon V(x))u=|u|^{p-2} u,$

where $a, b>0$ , and $2\textless p \textless6$ . Under suitable assumptions on $V$ , by using the Lyapunov-Schmidt reduction method, we obtain the existence of multi-bump solutions.

How to Cite this Article:
Y. Chen, Z. Yang, Existence of multi-bump solutions for a nonlinear Kirchhoff equation, J. Nonlinear Var. Anal. 8 (2024), 233-248.