A perturbation of nonlinear scalar field equations. (February 2019)

• Record Type: Journal Article
• Authors: Liu, Jiu; Liu, Tao; Liao, Jia-Feng
• Is Part Of: Nonlinear analysis. Volume 45(2019)
• Page Start: 531
• Page End: 541
• Publication Date: 2019-02
• Subjects: Schrödinger equations -- Variational methods -- Ground state solution; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.07.022
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In the paper, we consider the following Schrödinger equations − △ u + V ( x ) u = g ( u ), x ∈ R N, N ≥ 3, where g satisfies Berestycki–Lions conditions and V is a small perturbation. The assumptions on V are different from the ones in Azzollini and Pomponio (2009). By using the variational methods, we show the equation has a positive ground state solution.