Vector Solutions for Linearly Coupled Choquard Type Equations with Lower Critical Exponents. (21st December 2020)

• Record Type: Journal Article
• Authors: Wu, Huiling
• Other Names: Bellazzini Jacopo Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2020(2020)
• Publication Date: 2020-12-21
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2020/6623902
• Languages: English
• ISSNs: 1687-9120

Abstract

Abstract : The existence, nonexistence, and multiplicity of vector solutions of the linearly coupled Choquard type equations − Δ u + V 1 x u = I α ∗ u N + α / N u α / N − 1 u + λ v, x ∈ ℝ N, − Δ v + V 2 x v = I α ∗ v N + α / N v α / N − 1 v + λ u, x ∈ ℝ N, u, v ∈ H 1 ℝ N, are proved, where α ∈ 0, N, N ≥ 3, V 1 x V 2 x ∈ L ∞ ℝ N are positive functions, and I α denotes the Riesz potential.