The paper claims existence of multi-peak solutions with O(μ^{-1/2}) peaks for a slightly supercritical Hénon-type problem in the 3D unit ball, but the reduced system on which the proof depends has no positive solution as stated.
A Sobolev inequality with re- mainder term and critical equations on domains with topology for the polyharmonic operator
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Solutions with large number of peaks for a slightly supercritical nonlinear equation in dimension three
The paper claims existence of multi-peak solutions with O(μ^{-1/2}) peaks for a slightly supercritical Hénon-type problem in the 3D unit ball, but the reduced system on which the proof depends has no positive solution as stated.