Ground states to a Kirchhoff equation with fractional Laplacian

The aim of this paper is to deal with the Kirchhoff type equation involving fractional Laplacian operator

$$\left(\alpha +\beta {\int }_{{\mathbb{R}}^3}|(-\mathrm{\Delta }{)}^{\frac{s}{2}}\psi {|}^2\mathrm{d}x\right)(-\mathrm{\Delta }{)}^s\psi +\kappa \psi =|\psi {|}^{p-2}\psi \text{in}{\mathbb{R}}^3,$$

where $\alpha ,\beta ,\kappa >0$ are constants. By constructing a Palais-Smale-Pohozaev sequence at the minimax value $c_{mp}$, the existence of ground state solutions to this equation for all $p\in (2,2_s^{\ast })$ is established by variational arguments. Furthermore, the decay property of the ground state solution is also investigated.