Struwe compactness results for a critical $p-$Laplacian equation involving critical and subcritical Hardy potential on compact Riemannian manifolds

Abstract

Let $(M,g)$ be a compact Riemannian manifold. In this paper, we prove Struwe-type decomposition formulas for Palais-Smale sequences of functional energies corresponding to the equation: \begin{equation*} \Delta_{g,p}u-\frac{h(x)}{(\rho_{x_{o}}(x))^{s}}\left u\right ^{p-2}u =f(x)\left u\right ^{p^{\ast}-2}u, \end{equation*} where $\Delta_{g,p} $ is the $p-$Laplacian operator, $p^*=\frac{np}{n-p}$, $0