Some remarks on the solvability of non-local elliptic problems with the Hardy potential

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Caffarelli–Kohn–Nirenberg type inequalities of fractional order with applications (2016, methodology): “The fractional case with p = 2 was studied in [14] and [5].”
The effect of the Hardy potential in some Calder\'on-Zygmund properties for the fractional Laplacian (2015, methodology): “First, the following result holds (see [11, 20]).”
Borderline Variational Problems Involving Fractional Laplacians and Critical Singularities (2015, background): “These cases were also studied on smooth bounded domains (see for example [2], [3], [5], [15], [34] and the references therein).”
Semilinear problems for the fractional laplacian with a singular nonlinearity (2015, methodology): “Firstly, the approach of [9] based on the use of sub/supersolutions method still works in this context (see also [5, 6] where this monotonicity techniques are applied in the nonlocal framework).”
A critical fractional equation with concave-convex power nonlinearities (2013, methodology): “se the PS condition is easier to prove -it is indeed satisﬁed for any energy level- and the separation of solutions, presented in Lemma 2.3 below, is not needed. This approach has been carried out in [10] where the authors obtain the equivalent to Theorem 1.1 for a related problem using a technique ”