Positive clusters for smooth perturbations of a critical elliptic equation in dimensions four and five.

We construct clustering positive solutions for a perturbed critical elliptic equation on a closed manifold of dimension n = 4 , 5 . Such a construction is already available in the literature in dimensions n ≥ 6 (see for instance [10,14,30,32,36] ) and not possible in dimension 3 by [25] . This also provides new patterns for the Lin–Ni [26] problem on closed manifolds and completes results by Brézis and Li [8] about this problem. [ABSTRACT FROM AUTHOR]