Ground state solutions for a Choquard equation with lower critical exponent and local nonlinear perturbation. (July 2020)

• Record Type: Journal Article
• Authors: Wang, Xiaoping; Liao, Fangfang
• Is Part Of: Nonlinear analysis. Volume 196(2020)
• Publication Date: 2020-07
• Subjects: 35J20 -- 35J62 -- 35Q55; Choquard equation -- Lower critical exponent -- Local nonlinear perturbation -- Ground state solution -- Pohoz̆aev manifold; 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.2020.111831
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper deals with the following Choquard equation with a local nonlinear perturbation: − Δ u + u = I α ∗ | u | α N + 1 | u | α N − 1 u + f ( u ), x ∈ R N ; u ∈ H 1 ( R N ), where I α : R N → R is the Riesz potential, N ≥ 3, α ∈ ( 0, N ), the exponent α N + 1 is critical with respect to the Hardy–Littlewood–Sobolev inequality, and the nonlinear perturbation f is only required to satisfy some weak assumptions near 0 and ∞ . Our results improve the previous related ones in the literature.