Uniqueness and asymptotical behavior of solutions to a Choquard equation with singularity. (April 2020)

• Record Type: Journal Article
• Authors: Yu, Shengbin; Chen, Jianqing
• Is Part Of: Applied mathematics letters. Volume 102(2020)
• Publication Date: 2020-04
• Subjects: Choquard equation -- Singularity -- Variational method -- Asymptotic behavior; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2019.106099
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, we consider a nonautonomous Choquard equation with singularity − Δ u + V ( x ) u + λ ( I α ∗ | u | p ) | u | p − 2 u = f ( x ) u − γ, x ∈ R 3, u > 0, x ∈ R 3, where I α is the Riesz potential of order α ∈ ( 0, 3 ) and 1 + α 3 ≤ p < 3 + α, 0 < γ < 1 . Under certain assumptions on V and f, we show the existence and uniqueness of positive solution for λ > 0 by using variational method. We also study the asymptotic behavior of solutions as λ → 0 .