We exhibit a class of convex and nonsymmetric domains Ω in R~N, N ≥ 4, such that the slightly subcritical problem {-Δu = u~((N+2)/(N-2))-ε in Ω, u > 0 in Ω, u = 0 on (partial deriv)Ω does not have any solutions blowing up at more than one point in fi as e goes to zero. Moreover if Ω is a small perturbation of a convex and symmetric domain, we prove that such a problem has a unique solution provided ε is small enough.
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