Existence of positive solutions for a class of critical fractional Schrodinger-Poisson system with potential vanishing at infinity

In this paper, we study the following fractional Schrodinger-Poisson system { (-Delta)(s)u + V(x)u + phi u = K(x) f(u) + vertical bar u vertical bar(2)s(*-2)u, in R-3,R- (-Delta)(t)phi = u(2), in R-3,( ) where s is an element of (3/4, 1),t is an element of (0,1) are fixed constants, (-Delta)(s) is the fractional Laplace operator, 2(s)* = 6/3-2s, V and K are positive functions and f is continuous, superlinear at infinity with quasicritical growth. We show that the above equation has a positive solution via the variational method. (C) 2019 Elsevier Ltd. All rights reserved.