Existence of positive solutions for a problem with lack of compactness involving the p-Laplacian

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Multiplicity and Concentration of Positive Solutions for a Class of Quasilinear Problems (2011, background): “As mentioned above , the proof of the case ξ3 = 0 can be found in Alves [1]; thus we will consider only the case ξ3 > 0.”
A Global Compactness Result for the P-laplacian Involving Critical Nonlinearities (2010, background): “6 Proof. The case p 2 is treated in [ 1 ]. We assume that 1 1 ] when p > 2.”
The concentration-compactness principle for variable exponent spaces and applications (2009, unknown): “Just to cite a few, see [1, 2, 3, 7, 4, 11] but there is an impressive list of references on this.”
A priori estimates and application to the symmetry of solutions for critical $p$-Laplace equations (2014, background): “In case p 6 = 2, global compactness results in energy spaces in the spirit of Struwe [26] have been established in diﬀerent contexts by Alves [1] for equations posed in the whole R n , Saintier [23] in the case of a smooth, compact manifold, and Mercuri–Willem [20] and Yan [32] in the case of a…”