We study the existence of semiclassical states for a nonlinear Schrödinger-Poisson system that concentrate near critical points of the external potential and of the density charge function. We use a perturbation scheme in a variational setting, extending the results in [1]. We also discuss necessary conditions for concentration.

1 aIanni, Isabella1 aVaira, Giusi uhttps://www.math.sissa.it/publication/concentration-positive-bound-states-schr%C3%B6dinger-poisson-problem-potentials