The Nehari manifold for a fractional critical Choquard equation involving sign-changing weight functions. (March 2019)

• Record Type: Journal Article
• Authors: Lan, Fengqin; He, Xiaoming
• Is Part Of: Nonlinear analysis. Volume 180(2019)
• Page Start: 236
• Page End: 263
• Publication Date: 2019-03
• Subjects: Fractional Laplacian -- Variational methods -- Choquard equation -- Critical exponent -- Nehari 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.2018.10.010
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we prove the existence and multiplicity of nontrivial solutions for the following fractional Choquard equation with critical exponent ( − Δ ) s u = λ f ( x ) | u | q − 2 u + g ( x ) ∫ Ω | u | 2 μ, s ∗ | x − y | μ d y | u | 2 μ, s ∗ − 2 u in Ω u = 0, in R n ∖ Ω where Ω is a bounded domain in R n with smooth boundary, s ∈ ( 0, 1 ), 0 < μ < n, n > 2 s, 1 < q < 2 and 2 μ, s ∗ = ( 2 n − μ ) ∕ ( n − 2 s ) is the critical exponent in the sense of Hardy–Littlewood–Sobolev inequality. λ > 0 is a parameter and f, g : Ω ̄ → R are continuous functions but may change sign on Ω .