Multiplicity and Concentration of Solutions for Fractional Magnetic Schrödinger-Poisson Equation

In this paper, we consider the following fractional Schrödinger-Poisson equation with magnetic fields ^2 s (-) ₀ / ˢ u+V (x) u+^-2 (|x|^-1 *|u|²) u=f (|u|²) u in R³, where ε > 0 is a small parameter, V (x): R3 → R and A (x): R3 → R3 are continuous potentials. Under a local assumption on the potential V, by variational methods, penalization technique and Ljusternik-Schnirelmann theory, we obtain the multiplicity and concentration phenomena of nontrivial solutions of the above problem for ε > 0 small. In this problem, the function f is only continuous, which allow to consider larger classes of nonlinearities in the reaction.