Isolated singularities of solutions of certain quasi-linear elliptic inequalities

We provide a complete classification of the asymptotic behavior of isolated singularities for solutions satisfying $$0\le -{\mathrm{\Delta }}_{p}u(x)\le \tau u^{\frac{n(p-1)}{n-p}}(x),u(x)\ge 0,1<p<n,n\ge 2,$$where $u(x)\in C^2(B(0,1)\mathrm{\backslash }\{0\})$ and $B(0,1)\subset {\mathbb{R}}^n$.