An existence result for singular fractional Kirchhoff-Schr\"{o}dinger-Poisson system

Abstract

In this paper, we study the existence of infinitely many weak solutions to a fractional Kirchhoff-Schr\"{o}dinger-Poisson system involving the weak singularity, i.e. when $0<\gamma<1$. Further, we obtain the existence of a solution with the strong singularity, i.e. when $\gamma>1$. We employ variational techniques to prove the existence and multiplicity results. Moreover, a $L^{\infty}$ estimate is obtained by using the Moser iteration method.