We revisit the well-known Brezis-Nirenberg problem {- Delta u = u (N+2/N-2) + epsilon u, in Omega, u > 0, in Omega, u = 0, on partial derivative Omega, where epsilon > 0 and Omega subset of RN are a smooth bounded domain with N >= 3. The existence of multi-bump solutions to above problem for small parameter epsilon > 0 was obtained by Musso and Pistoia (Indiana Univ Math J 51:541-579, 2002). However, to our knowledge, whether themulti-bump solutions are non-degenerate that is open. Here, we give some straightforward answer on this question under some suitable assumptions for the Green's functi...
