Existence of solutions for a class of elliptic equations in RNRN with vanishing potentials

In this paper we investigate the existence of positive solution for the following class of elliptic equation−Δu+V(x)u=f(u)in RN, where f has a subcritical growth and V   is a nonnegative potential, which can vanish at infinity, that is, V(x)→0V(x)→0 as |x|→∞|x|→∞, or shortly, V(∞)=0V(∞)=0.