A global compactness result for singular elliptic problems involving critical Sobolev exponent

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A note on the sign-changing solutions to elliptic problems with critical Sobolev and Hardy terms $ (2003, methodology): “Recently, we established a global compactness theorem for problem (1) by applying rescaling arguments in [3].”
Existence and non-existence of solutions to elliptic equations related to the Caffarelli–Kohn–Nirenberg inequalities (2007, background): “5)  −∆u = μ u |x|2 + |x|βup(β)−1 + f(x, u), x ∈ Ω, u(x) = 0, x ∈ ∂Ω, where 0 ≤ μ < (N − 2)(2)/4, p(β) = 2(N + β)/(N − 2), −2 < β ≤ 0, f(x, u) is a subcritical perturbation; see [1, 8, 10, 11, 15, 19, 20, 23, 24, 25, 26] et al.”