Fractional Schrödinger-Poisson systems with weighted Hardy potential and critical exponent

Abstract

In this article we consider the fractional Schrödinger-Poisson system (-Δ)su - μ Φ(x/|x|)/|x|2s u + λφu = |u|2*s-2u, in ℝ3, (-Δ)tφ = u2, in ℝ3, where s ∈ (0, 3/4), t ∈ (0, 1), 2t + 4s = 3, λ > 0 and 2*s = 6/(3-2s) is the Sobolev critical exponent. By using perturbation method, we establish the existence of a solution for λ small enough.