On the radial solutions of a p-Laplace equation with the Hardy potential

In this paper, we study the asymptotic behavior of radial solutions of the following quasi-linear equation with the Hardy potential $\Delta_p u+h(|x|)|u|^{p-2}u=0$, $x\in \mathbb{R}^{N}-\{0\}$, where $2<p<N$, $h$ is a radial function on $\mathbb{R}^{N}-\{0\}$ such that $h(|x|)=\gamma|x|^{-p}$, $\gamma>0$ and $\Delta_p u=\operatorname{div}\left(|\nabla u|^{p-2}\nabla u\right)$ is the $p$-Laplacian operator.  The study strongly depends on the sign of $\gamma-(\sigma/p^\ast)^p$ where $\sigma=(N-p)/(p-1)$ and $p^\ast=p/(p-1)$.