Arbitrary number of positive solutions for an elliptic problem with critical nonlinearity

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Infinitely many solutions for the prescribed scalar curvature problem on SN (2010, unknown): “Similar weighted maximum norm has been used in [13],[27]–[ 29 ].”
A Neumann problem with critical exponent in nonconvex domains and Lin-Ni’s conjecture (2010, methodology): “From Lemma 3.2, using the same argument as in the proof of Proposition 4.1 in [41] and Proposition 3.1 in [52], we can prove the following result: We have Proposition 3.4.”