Schrödinger-Poisson systems with singular potential and critical exponent

Abstract

In this article we study the Schrödinger-Poisson system -Δu + V(|x|)u + λφu = ƒ(u), x ∈ ℝ3, -Δφ = u2, x ∈ ℝ3 where V is a singular potential with the parameter α and the nonlinearity ƒ satisfies critical growth. By applying a generalized version of Lions-type theorem and the Nehari manifold theory, we establish the existence of the nonnegative ground state solution when λ = 0. By the perturbation method, we obtain a nontrivial solution to above system when λ ≠ 0.