Semiclassical solutions for Choquard equations with Berestycki–Lions type conditions. (November 2019)

• Record Type: Journal Article
• Authors: Zhang, Jing; Wu, Qingfang; Qin, Dongdong
• Is Part Of: Nonlinear analysis. Volume 188(2019)
• Page Start: 22
• Page End: 49
• Publication Date: 2019-11
• Subjects: primary 35J61 -- secondary 35B25 35B33; Choquard equation -- Multiple semiclassical solutions -- Berestycki–Lions type conditions; 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.2019.05.016
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper is concerned with existence of multiple semiclassical states for a class of Choquard equation. Under the classic Berestycki–Lions type assumptions assumed on the nonlinearity, we obtain multiplicity of semiclassical solutions for the equation by using a method of penalization argument. We study further the concentration phenomena of such solutions and show that they converge to the least energy solutions of the associated limit problem as the parameter ε goes to 0.