Positive solutions of an asymptotically periodic Schrödinger–Poisson system with critical exponent. (December 2016)

• Record Type: Journal Article
• Authors: Liu, Haidong
• Is Part Of: Nonlinear analysis. Volume 32(2016)
• Page Start: 198
• Page End: 212
• Publication Date: 2016-12
• Subjects: Generalized Schrödinger–Poisson system -- Asymptotically periodic -- Critical exponent -- Mountain pass theorem -- Concentration-compactness principle; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.04.007
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: Existence of one positive solution of the generalized Schrödinger–Poisson system { − Δ u + V ( x ) u − K ( x ) ϕ | u | 3 u = f ( x, u ) in R 3, − Δ ϕ = K ( x ) | u | 5 in R 3, where V, K, f are asymptotically periodic functions of x, is proved by the mountain pass theorem and the concentration-compactness principle. The system with subcritical nonlocal term has been studied extensively in the last twenty years, while the system with critical nonlocal term has seldom been studied. It turns out that new techniques are needed in dealing with the case of critical nonlocal term.