We consider the equation

If Ω is of class , we show that this problem has a non-trivial solution u λ for each λ ∊ (8π, λ*). The value λ* depends on the domain and is bounded from below by 2 j 0 2 π, where j 0 is the first zero of the Bessel function of the first kind of order zero (λ*≥ 2 j 0 2 π > 8 π). Moreover, the family of solution u λ blows-up as λ → 8 π.