Electron. J. Differential Equations, Vol. 2024 (2024), No. 10, pp. 114.
Ground state solutions for fractional Kirchhoff type equations with critical growth
Kexue Li
Abstract:
We study the nonlinear fractional Kirchhoff problem
$$\displaylines{
\Big(a+b\int_{\mathbb{R}^3}(\Delta)^{s/2}u^2dx\Big)
(\Delta)^su+u=f(x,u)+u^{2_s^{\ast}2}u \quad \text{in }\mathbb{R}^3,\\
u\in H^s(\mathbb{R}^3),
}$$
where \(a,b>0\) are constants, \(s(3/4,1)\), \(2_s^{\ast}=6/(32s)\), \((\Delta)^s\)
is the fractional Laplacian. Under some relaxed assumptions on \(f\),
we prove the existence of ground state solutions.
Submitted February 13, 2023. Published January 29, 2024.
Math Subject Classifications: 35R11, 35B50, 34A08.
Key Words: Ground state solution; fractional Kirchhoff equation; critical exponent.
DOI: 10.58997/ejde.2024.10
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Kexue Li
School of Mathematics and Statistics
Xi'an Jiaotong University
Xi'an, 710049, China
email: kxli@mail.xjtu.edu.cn

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