Ground state solutions for fractional Choquard equations involving upper critical exponent. (August 2020)

• Record Type: Journal Article
• Authors: Li, Quanqing; Teng, Kaiming; Zhang, Jian
• Is Part Of: Nonlinear analysis. Volume 197(2020)
• Publication Date: 2020-08
• Subjects: 35J20 -- 35J70 -- 35P05; Fractional Choquard equation -- Ground state solutions -- Nehari method; 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.2020.111846
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this article, we study the following fractional Choquard equation involving upper critical exponent ( − Δ ) s u + V ( x ) u = λ f ( x, u ) + [ | x | − μ ∗ | u | 2 μ, s ∗ ] | u | 2 μ, s ∗ − 2 u, x ∈ R N, where λ > 0, 0 < s < 1, ( − Δ ) s denotes the fractional Laplacian of order s, N > 2 s, 0 < μ < 2 s and 2 μ, s ∗ = 2 N − μ N − 2 s . When V and f are asymptotically periodic in x, we prove that the equation has a ground state solution for large λ by Nehari method.