Ground state of Kirchhoff type fractional Schrödinger equations with critical growth

In this paper, we study the critical Kirchhoff type fractional Schrödinger equation:(0.1)(1+α∫R3∫R3|u(x)−u(y)|2|x−y|3+2sdxdy)(−Δ)su+u=βf(u)+u2s⁎−1inR3, where s∈(0,1) and 2s⁎=63−2s. We establish the Pohozǎev type identity of (0.1). When s∈[34,1), under some conditions on α, β and f(u), we obtain some results on the existence of ground state solutions. When s∈(0,34], we also prove the non-existence result. In particular, when α=0, we obtain an existence result.