Blow-up examples for second order elliptic PDEs of critical Sobolev growth

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Blow-up solutions for asymptotically critical elliptic equations on Riemannian manifolds (2009, background): “When (1.2) is not anymore an equality, the question of compactness of equations like (1.1) have been investigated, among other possible references, by Druet [6, 7], Druet–Hebey [8], and Li– Zhu [17].”
Concentration–compactness phenomena in the higher order Liouville's equation☆ (2008, unknown): “Contrary to what happens for the Yamabe equation (see [Dru1], [Dru2], [ DH ] and [DHR]), the concentration points of S in Theorem 2 are isolated, as already proved in [DR] in dimension 4. In fact, a priori one could expect to have”
Blow-up phenomena for the Yamabe equation II (2009, background): “Hebey [7] have constructed blow-up examples for perturbations of (1) (see also [8]).”