Existence of multiple semiclassical solutions for a critical Choquard equation with indefinite potential. (June 2020)

• Record Type: Journal Article
• Authors: Gao, Fashun; Yang, Minbo; Zhou, Jiazheng
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: 35J20 -- 35J60 -- 35A15; Critical Choquard equation -- Semiclassical states -- Sign-changing potentials -- Hardy–Littlewood–Sobolev inequality; 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.2020.111817
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the existence and multiplicity of semiclassical states for the Choquard equation with critical growth − ε 2 Δ u + V ( x ) u = ( ∫ R N G ( y, u ( y ) ) | x − y | μ d y ) g ( x, u ) in R N, where N ≥ 3, 0 < μ < min { 4, N }, V ( x ) is sign changing and G is the primitive of g which is of critical growth due to the well known Hardy–Littlewood–Sobolev inequality. Under suitable assumptions on V and g, we prove the existence and multiplicity of semiclassical states by critical point theory.