Ground state solutions for fractional Kirchhoff type equations with critical growth

Abstract

We study the nonlinear fractional Kirchhoff problem $$ \Big(a+b\int_{\mathbb{R}^3}|(-\Delta)^{s/2}u|^2dx\Big) (-\Delta)^su+u=f(x,u)+|u|^{2_s^{\ast}-2}u \quad \text{in }\mathbb{R}^3, $$ $$ u\in H^s(\mathbb{R}^3), $$ 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. For more inofrmation see https://ejde.math.txstate.edu/Volumes/2024/10/abstr.html