Multiplicity and Concentration Results for Fractional Schrodinger-Poisson Equations with Magnetic Fields and Critical Growth

We deal with the following fractional Schrodinger-Poisson equation with magnetic field epsilon 2s(-Delta)A/epsilon su+V(x)u+epsilon-2t(|x|2t-3*|u|2)u=f(|u|2)u+|u|2s*-2uin Double-struck capital R3,{R}<^>{3}, where epsilon > 0 is a small parameter, s is an element of(34,1), t is an element of (0, 1), 2s*=63-2s is the fractional critical exponent, (-Delta)As is the fractional magnetic Laplacian, V:Double-struck capital R3 -> Double-struck capital R is a positive continuous potential, A:Double-struck capital R3 -> Double-struck capital R3 is a smooth magnetic potential and f:Double-struck capital R -> Double-struck capital R is a subcritical nonlinearity. Under a local condition on the potential V, we study the multiplicity and concentration of nontrivial solutions as epsilon -> 0. In particular, we relate the number of nontrivial solutions with the topology of the set where the potential V attains its minimum.