Concentration results for a magnetic Schrodinger-Poisson system with critical growth

This paper is concerned with the following nonlinear magnetic Schrodinger-Poisson type equation { (epsilon/i del - A(x)))(2) u + V(x)u + epsilon(-2)(vertical bar x vertical bar(-1) * vertical bar u vertical bar(2)) u + vertical bar u vertical bar(4)u in R-3, u is an element of H-1 (R-3, C), where epsilon > 0, V : R-3 and A : R-3 -> R-3 are continuous potentials, f : R -> R is a subcritical nonlinear term and is only continuous. Under a local assumption on the potential V, we use variational methods, penalization technique and Ljusternick-Schnirelmann theory to prove multiplicity and concentration of nontrivial solutions for epsilon > 0 small.