The nontrivial solutions for fractional Schrodinger-Poisson equations with magnetic fields and critical or supercritical growth

In this paper, we study the following fractional Schrodinger-Poisson equation with magnetic field (-Delta)(A)(s)u + V(x)u + (vertical bar x vertical bar(2t-3) * vertical bar u vertical bar(2))u = f(x, vertical bar u vertical bar(2))u + lambda vertical bar u vertical bar(p-2)u in R-3, where lambda > 0, s is an element of (3/4, 1), t is an element of (0, 1), p >= 2(s)* = 6/3-2s, (-Delta)(A)(s) is the fractional magnetic Laplacian, V : R-3 -> R is a positive continuous potential, A : R-3 -> R-3 is a smooth magnetic potential. We mainly prove that the above equation has a nontrivial solution for small lambda > 0 and p > 2(s)*. (C) 2021 Published by Elsevier Ltd.