Multiplicity and concentration of solutions for a fractional Schrödinger–Poisson system with sign-changing potential

Abstract

This paper is concerned with the following fractional Schrödinger–Poisson system: where is a parameter, , , , is allowed to be sign-changing and f is an indefinite function. We require that with having a potential well Ω whose depth is controlled by λ and for all . Under some suitable assumptions on and , we prove that the above system has at least two nontrivial solutions. Moreover, the phenomenon of concentration of the solutions is also explored.