This paper is concerned with the existence of positive solutions for the following problem: -div(|Du|^p-2Du)+k (x) u^P-1=K(x)u^P-1+g(x,u)，u∈W^1,P (R^N),4≤P²≤N,P=NP/N-p，where g (x,u) is a lower-order perturbation of u^p-1. It is the continuation of the zero-perturbation case.