In this paper we consider the problem (Formula presented.) where Ω is a bounded smooth domain in ℝN, N ≥ 3, the function a∈ C2(Ω) is strictly positive on (Formula presented.) and α is a positive real number which is not an even integer. Here ɛ is a positive small parameter. We give some sufficient conditions on the function a which ensure existence of solutions to (1) blowing up at the point ξ as ɛ goes to zero.