Fractional Schrödinger–Poisson system with critical growth and potentials vanishing at infinity

Abstract In this paper, we are concerned with the existence of positive solutions for a class of fractional Schrödinger–Poisson system with critical nonlinearity and multiple competing potentials, which may decay and vanish at infinity. Under some local conditions, we show the existence and concentration of positive solutions by using the modified penalization method and concentration–compactness principle.