Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 10, pp. 1-14.

Title: Ground state solutions for fractional Kirchhoff type equations with critical growth
       
Author: Kexue Li (Xi'an Jiaotong Univ., Xi'an, China)

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, $s(3/4,1)$, $2_s^{\ast}=6/(3-2s)$, $(-\Delta)^s$
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.