A global compactness result for quasilinear elliptic problems with critical Sobolev nonlinearities and Hardy potentials on R^N

In this article, we study the elliptic equation with critical Sobolev nonlinearity and Hardy potentials $$ (-\Delta)_p u+a(x) |u|^{p-1}u-\mu\frac{|u|^{p-1}u}{|x|^p} =|u|^{p^*-2}u+f(x,u),\quad u \in W^{1,p}(\mathbb{R}^N), $$ where \(0<\mu<\min\{\frac{(N-p)^p}{p^p}, \frac{N^{p-1}(N-p^2)}{p^p}\}\), \(p^*=\frac{Np}{N-p}\) is the critical Sobolev exponent. Through a compactness analysis of the associated functional operator, we obtain the existence of positive solutions under certain assumptions on \(a(x)\) and \(f(x,u)\). For more information see https://ejde.math.txstate.edu/Volumes/2024/79/abstr.html