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In this paper, we study an integral equation of Landau-Lifschitz-type involving the Riesz potential u(x)=+C_*∫Rⁿu(y)(|∇ u(y)|²+|uₖ(y)|²)-uₖ(y)eₖ|x-y|n-αdy, where ∈ Rᵏ is a constant vector, C_* ≠ 0 is a constant, uⁿ → Sᵏ⁻¹:==(u₁,u₂,⋯,uₖ) ∈ Rᵏ;|u|=1\, k ≥ 1, n ≥ 2, and $0<α
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Tiantian Zhou (2026) studied this question.
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