Abstract We are concerned with the study of C^2, ₋₎₂ C loc 2, γ -positive solutions to the Choquard equation - u= (|x|^- *uᵖ) uq in RN_+= R^N-1 (0, ) \, , N 2, - Δ u = λ (| x | - α ∗ u p) u q in R + N = R N - 1 × (0, ∞), N ≥ 2, subject to the Robin boundary condition u+ u =g β u + ∂ u ∂ ν = g on RN_+ ∂ R + N. Here p, q, >0 p, q, λ > 0, (0, N) α ∈ (0, N), R β ∈ R and 0 g C^1, ₋₎₂ (R^N-1) 0 ≤ g ∈ C loc 1, γ
Marius Ghergu (Sat,) studied this question.
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