Super-critical boundary bubbling in a semilinear Neumann problem

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Sign Changing Tower of Bubbles for an Elliptic Problem at the Critical Exponent in Pierced Non-Symmetric Domains (2010, background): “The result in [29], as well as in other related problems where construction of tower of bubbles is obtained [14, 15, 16, 32], rely strongly on the assumption of symmetry of the domain.”
Blow-up solutions for asymptotically critical elliptic equations on Riemannian manifolds (2009, background): “Recent references on (1.6) are by del Pino–Musso–Pistoia [20] and Rey–Wei [21,22] where blowing-up families of solutions are proved to exist with blow-up points located on the boundary and determined by the mean curvature of ∂Ω.”
Tower of bubbles for almost critical problems in general domains (2010, background): “The proof of the results contained in [5], [6], [8], [16] is based on a version of the Liapunov-Schmidt reduction (see [9]) in the class of radially symmetric functions with bounded weighted L∞-norm (see also [7]).”