Electron. J. Differential Equations, Vol. 2022 (2022), No. 61, pp. 1-14.

Ground state solutions for fractional p-Kirchhoff equation

Lixiong Wang, Haibo Chen, Liu Yang

Abstract:
We study the fractional p-Kirchhoff equation

where $(-\Delta)_p^s$ is the fractional p-Laplacian operator, a and b are strictly positive real numbers, $s \in (0,1)$, $ 1 < p< \frac{N}{s}$, and $p<q<p^*_s-2$ with $p^*_s=\frac{Np}{N-ps}$. By using the variational method, we prove the existence and uniqueness of global minimum or mountain pass type critical points on the $L^p$-normalized manifold $S(c):=\big\{u\in W^{s,p}(\mathbb{R}^N): \int_{\mathbb{R}^N} |u|^pdx=c^p\big\}$.

Submitted April 11, 2022. Published August 19, 2022.
Math Subject Classifications: 35J20, 35J60.
Key Words: Variational method; L^p-normalized critical point; fractional; p-Kirchhoff equation; uniqueness.
DOI: https://doi.org/10.58997/ejde.2022.61

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Lixiong Wang
School of Mathematics and Statistics
Central South University
Changsha, 410083 Hunan, China
email: wanglixiong2018@163.com
Haibo Chen
School of Mathematics and Statistics
Central South University
Changsha, 410083 Hunan, China
email: math_chb@163.com
Liu Yang
College of Mathematics and Statistics
Hengyang Normal University
Hengyang, 421008 Hunan, China
email: yangliuyanzi@163.com

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