Existence of positive solutions for a critical nonlinear Schrodinger equation with vanishing or coercive potentials

In this paper we investigate the existence of the positive solutions for the following nonlinear Schr"odinger equation $$-\mathrm{△}u+V(x)u=K(x)\mathrm{\mid }u{\mathrm{\mid }}^{p-2}uin{\mathbb{R}}^N$$ where $V(x)\sim a\mathrm{\mid }x{\mathrm{\mid }}^{-b}$ and $K(x)\sim \mu \mathrm{\mid }x{\mathrm{\mid }}^{-s}$ as $\mathrm{\mid }x\mathrm{\mid }\to \mathrm{\infty }$ with $0<a,\mu <+\mathrm{\infty }$, $b<2,$ $b\mathrm{\ne }0$, $0<\frac{s}{b}<1$ and $p=2(N-2s\mathrm{/}b)\mathrm{/}(N-2)\mathrm{.}$