Ground states of a class of gradient systems of Choquard type with general nonlinearity. (December 2021)

• Record Type: Journal Article
• Authors: Sun, Wei; Chang, Xiaojun
• Is Part Of: Applied mathematics letters. Volume 122(2021)
• Publication Date: 2021-12
• Subjects: Ground state solutions -- Gradient systems -- Choquard equations -- Berestycki–Lions type conditions -- Variational methods; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107503
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We consider the following gradient system of Choquard type − Δ u 1 + u 1 = ( I μ ∗ F ( u 2 ) ) f ( u 1 ) in R N, − Δ u 2 + u 2 = ( I μ ∗ F ( u 1 ) ) f ( u 2 ) in R N, where N ≥ 3 and I μ ( 0 < μ < N ) is a Riesz potential. By the variational methods, we prove the existence of ground state solutions under the Berestycki–Lions type conditions.