where Ω is a smooth domain in R , N ≥ 3, and p ≥ 2N/(N − 2) (the critical Sobolev exponent for the embedding H 0 (Ω) ↪→ L(Ω)). Many papers have been devoted to such problems (see [2], [5], [6], [10]–[12], [14], [15], [18]–[23], [25], [27], [28], and the references therein). Here the lack of compactness, due to the presence of the critical exponent, is just… (More)