Electron. J. Differential Equations

Electron. J. Differential Equations, Vol. 2024 (2024), No. 10, pp. 1-14.

Ground state solutions for fractional Kirchhoff type equations with critical growth
Kexue Li

Abstract:
We study the nonlinear fractional Kirchhoff problem

\begin{matrix} (a + b \int_{R^{3}} | (- Δ)^{s / 2} u |^{2} d x) (- Δ)^{s} u + u = f (x, u) + | u |^{2_{s}^{*} - 2} u in R^{3}, \\ u \in H^{s} (R^{3}), \end{matrix}

where

a, b > 0

are constants,

s (3 / 4, 1)

2_{s}^{*} = 6 / (3 - 2 s)

(- Δ)^{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

	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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Ground state solutions for fractional Kirchhoff type equations with critical growth Kexue Li

Ground state solutions for fractional Kirchhoff type equations with critical growth
Kexue Li