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

摘要

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 Brezis and Li [8] about this problem. (C) 2018 Elsevier Inc. All rights reserved.