In this article we study the Schrödinger-Poisson system−∆ u+ V (| x|) u+ λφu= f (u), x∈ R3,−∆ φ= u2, x∈ R3, where V is a singular potential with the parameter α and the nonlinearity f 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.
Liu, Senli, Haibo Chen, and Zhaosheng Feng. "Schrödinger-Poisson systems with singular potential and critical exponent." Electronic Journal of Differential Equations 2020.130 (2020): 1-17.
Electronic Journal of Differential Equations