Multiple solutions for fractional Schrödinger–Poisson system with critical or supercritical nonlinearity

Abstract

In this paper, we study the following fractional Schrödinger–Poisson system (−Δ)su+V(x)u+ϕu=f(x,u)+λ|u|p−2u,inR3,(−Δ)tϕ=u2,inR3,where s∈(34,1), t∈(0,1), λ>0 is a real parameter, (−Δ)s is the fractional Laplace operator, p≥2s∗=63−2s. Under some suitable assumptions on V and f, by using Moser iterative method and truncation technique, we prove that the above equation has a ground state solution and a sign-changing solution.