Multiplicity and concentration results for a class of critical fractional Schrodinger Poisson systems via penalization method

We deal with the multiplicity and concentration of positive solutions for the following fractional Schrodinger-Poisson-type system with critical growth: {epsilon(2s)(-Delta)(s)u + V(x) + phi u=f(u) + vertical bar u vertical bar(2s)*(-2u) in R-3, epsilon(2t)(-Delta)(t)phi=u(2 )in R-3, where epsilon > 0 is a small parameter, s is an element of (3/4, 1), t is an element of (0, 1), (-Delta)(alpha), with alpha is an element of {s, t}, is the fractional Laplacian operator, V is a continuous positive potential and f is a superlinear continuous function with subcritical growth. Using penalization techniques and Ljusternik-Schnirelmann theory, we investigate the relation between the number of positive solutions with the topology of the set where the potential attains its minimum value.