Multiplicity of concentrating positive solutions for Schrödinger-Poisson equations with critical growth

In this paper we deal with a nonlinear Schrödinger-Poisson equation involving critical Sobolev exponent. Under a local condition imposed on the potential, we relate the number of positive solutions with the topology of the set where the potential attains its minimum values. In the proofs we apply Szulkin and Weth's generalized Nehari manifold methods, penalization techniques and Ljusternik-Schnirelmann theory.