We describe all nontrivial nonnegative solutions to the problem cases -Δ u = a u^n+2n-2 &in \ H, ∂ u ∂ ν = bu^nn-2 &on \ ∂ H, cases where H is the half space of Rⁿ (n≥3).
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Chipot et al. (1996) studied this question.
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