Multiple small solutions for some Schrödinger–Poisson systems. (April 2015)

• Record Type: Journal Article
• Authors: Zhang, Qingye; Xu, Bin
• Is Part Of: Nonlinear analysis. Volume 117(2015)
• Page Start: 200
• Page End: 210
• Publication Date: 2015-04
• Subjects: 35J20 -- 35J65 -- 35J60; Schrödinger–Poisson system -- Symmetric mountain pass lemma -- Variational method; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.01.009
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study the existence of infinitely many solutions for the following nonlinear Schrödinger–Poisson system { − △ u + V ( x ) u + ϕ u = f ( x, u ), x ∈ R 3, − △ ϕ = u 2, lim | x | → ∞ ϕ ( x ) = 0, where the nonlinear term f ( x, u ) is only locally defined for | u | small and satisfies some mild conditions.