Ground state of Kirchhoff type fractional Schrodinger equations with critical growth

In this paper, we study the critical Kirchhoff type fractional Schrodinger equation: (1+alpha integral(3)(R)integral(3)(R) |u(x) - u(y)|(2)/|x-y|(3-2s) dxdy) (-Delta)(s)u + u = beta f(u) + u(2*)s 1 in R-3, (0.1) where s is an element of (0, 1) and 2(S)(*) = 6/3-2s. We establish the Pohozaev type identity of (0.1). When s is an element of[3/4, 1), under some conditions on alpha, beta and f (u), we obtain some results on the existence of ground state solutions. When s is an element of (0, 3/4], we also prove the non-existence result. In particular, when alpha = 0, we obtain an existence result. (C) 2018 Elsevier Inc. All rights reserved.