Ground state solution for a Schrödinger–Poisson equation with critical growth. (April 2018)

• Record Type: Journal Article
• Authors: Liu, Jingmei; Qian, Aixia
• Is Part Of: Nonlinear analysis. Volume 40(2018)
• Page Start: 428
• Page End: 443
• Publication Date: 2018-04
• Subjects: Schrödinger–Poisson equation -- Ground state solution -- Critical growth -- Mountain pass theorem; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.09.008
• Languages: English
• ISSNs: 1468-1218

Abstract

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.