Multiplicity and concentration of solutions to the nonlinear magnetic Schrodinger equation

In this paper, we study the following nonlinear magnetic Schrodinger equation where epsilon is a positive parameter, and V : RN. R, A : RN. RN are continuous potentials. Under a local assumption on the potential V, by combining variationalmethods, penalization techniques, and the Ljusternik-Schnirelmann theory, we prove multiplicity and concentration properties of solutions for e > 0 small. In our problem, the function f is only continuous, which allows to consider larger classes of nonlinearities in the reaction.