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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.

Vector Solutions for Linearly Coupled Choquard Type Equations with Lower Critical Exponents