Positive and nodal ground state solutions for a critical Schrödinger-Poisson system with indefinite potentials

Abstract

We consider the Schrödinger-Poisson system{−Δu+V(x)u+K(x)ϕu=a(x)|u|p−2u+|u|4u,x∈R3,−Δϕ=K(x)u2,x∈R3, where 4<p<6 and the potentials V, a are allowed to change their signs. Under some reasonable assumptions on V, K and a, we apply the constraint minimization argument to establish the existence of positive ground state solutions and ground state nodal solutions.