Multiple clustered layer solutions for semilinear Neumann problems on a ball

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Monotonicity constraints and supercritical Neumann problems (2011, unknown): “…provided by these papers. contrast, nonau-tonomous problems, where a is not constant, and even with power nonlinearities, do not seem to have been deeply investigated in the supercritical case (with the exception of singularly perturbed problems, see for example [4] and the references therein .”
Chapter 6 Existence and stability of spikes for the Gierer-Meinhardt system (2008, background): “Third, if we vary R from 0 to +∞, what is the relation between the layered solution constructed in [ 52 ] for the single equation (2.4) and the solutions in Theorem 6.1?”
The Toda System and Clustering Interfaces in the Allen–Cahn equation (2008, background): “In the one-dimensional or radial cases, concentration in the form of clusters of transition layers or spikes has already been observed in various problems in the literature, see [4,10,11,13,27,28,32,33], phenomena in accordance with higherdimensional multi-spike clustering as predicted in [20].”
Some new entire solutions of semilinear elliptic equations on Rn (2009, result): “We also refer to the papers [ 45 ], [50], [57] for related results.”
Concentration at curves for a singularly perturbed Neumann problem in three-dimensional domains (2005, unknown): “Other results regarding concentration at higher dimensional sets are given in [3], [4], [5], [6], [9], [ 30 ] under some symmetry assumptions.”