Liu, SenliChen, HaiboFeng, Zhaosheng2021-10-132021-10-132020-12-26Liu, S., Chen, H., & Feng, Z. (2020). Schrödinger-Poisson systems with singular potential and critical exponent. <i>Electronic Journal of Differential Equations, 2020</i>(130), pp. 1-17.1072-6691https://hdl.handle.net/10877/14641In 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.Text17 pages1 file (.pdf)enAttribution 4.0 InternationalSchrödinger-Poisson systemLions-type theoremSingular potentialGround state solutionCritical exponentArticle