Existence of positive solutions for a class of critical fractional Schrödinger–Poisson system with potential vanishing at infinity

Abstract

In this paper, we study the following fractional Schrödinger–Poisson system (−Δ)su+V(x)u+ϕu=K(x)f(u)+|u|2s∗−2u,inR3,(−Δ)tϕ=u2,inR3, where s∈(34,1),t∈(0,1) are fixed constants, (−Δ)s is the fractional Laplace operator, 2s∗=63−2s, V and K are positive functions and f is continuous, superlinear at infinity with quasicritical growth. We show that the above equation has a positive solution via the variational method.