School of Mathematics and Statistics
Xi'an Jiaotong University
Xi'an, 710049, China
email: kxli@mail.xjtu.edu.cn
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, \(s(3/4,1)\), \(2_s^{\ast}=6/(3-2s)\), \((-\Delta)^s\)
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.
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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