“Bubble-tower” radial solutions in the slightly supercritical Brezis–Nirenberg problem

In this paper, we consider the Brezis–Nirenberg problem in dimension N 4, in the supercritical case. We prove that if the exponent gets close to and if, simultaneously, the bifurcation parameter tends to zero at the appropriate rate, then there are radial solutions which behave like a superposition of bubbles, namely solutions of the form where Mj→+∞ and Mj=o(Mj+1) for all j. These solutions lie close to turning points “to the right” of the associated bifurcation diagram.