Ground state solution for a Schrödinger–Poisson equation with critical growth. (April 2018) - Liu, Jingmei; Qian, Aixia
Abstract: In this paper, we consider the following nonlinear Schrödinger–Poissonequation − △ u + V ( x ) u + K ( x ) ϕ u = μ a ( x ) | u | q − 1 u + | u | 4 u, in R 3, − △ ϕ = K ( x ) u 2, in R 3, where μ is a positive parameter. Under certain assumptions on V ( x ), K ( x ) and a ( x ), we prove that for every μ > 0 and q ∈ ( 2, 5 ), the Schrödinger–Poisson equation with critical growth has at least a positive ground state solution by variational method.